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The Generation Game

The Generation Game is a British game show produced by the BBC in which four teams of two people from the same family, but different generations, compete to win prizes.

The game
There are eight competitors, hence the catchphrase "Let's meet the eight who are going to generate" used in earlier series by Bruce Forsyth. The couples were a generation apart and in later series, but not originally, of different genders. Most of the time it was mother/son, father/daughter. Sometimes aunt/nephew and uncle/niece played. In the first two rounds, two couples compete against each other in two games. One game usually involves first seeing a skilled professional construct or perform something, such as pottery or dancing. The contestants attempt to do the same, and a score is given by the professional. The other game usually involves more of a quiz element, such as identifying pieces of music. At the end of each of the first two rounds, the couple with the lower score is eliminated.

The two highest-scoring couples compete against each other in the final (or End Game as Larry Grayson called it). This is often a big set-piece performance; in the series presented by Bruce Forsyth it was usually a drama or farce (in which many elements were deliberately choreographed to go wrong in order to generate more comedy), in later programmes a musical or dance performance. The couple that scores the highest go through to the final 'conveyor belt'. Originally, this was scored the same way in the first rounds, but when Davidson took over, the winner was decided by an audience vote.

At the end of the show, one member (both members during the second Forsyth era) of the victorious team watches prizes pass on a conveyor belt, and wins as many as could be recalled in 45 seconds (20 seconds per teammate during the second Forsyth era), with some items awarding a bonus prize if the contestant or team recalls that item. A trademark of the show is that a cuddly toy is always among the prizes. This led to an affectionate joke: "Dinner service...fondue set...Cuddly toy! Cuddly toy!", which is sometimes quoted when the show is mentioned. The audience and the host shout out the names of the prizes, especially in later series, allowing the contestants to carry away large numbers of items. Towards the end of the Davidson run, an added twist involved four prizes being referred to as "phantom prizes", if the contestant was to mention those, gunge would be hurled at them every time one was recalled.

In the Davidson run, if contestants correctly recalled 15 of the 20 prizes in 45 (later 60) seconds, they won everything and a bonus prize, usually a holiday. In series 6, each point scored by the winning team became one second.

1971–1977: Origins and first Bruce Forsyth era
The show is based on the Dutch TV show Één van de acht ("One of the Eight"), the format devised in 1969 by Theo Uittenbogaard for VARA Television. Mies Bouwman, a Dutch talk show host and presenter of the show, came up with the idea of the conveyor belt. She had seen it on a German programme and wanted to incorporate it into the show.

Another antecedent for the game show was Sunday Night at the London Palladium on ATV, which had a game called Beat the Clock, taken from an American game show of the same name. It featured married couples playing silly games within a certain time to win prize money. This was hosted by Bruce Forsyth from 1958, and he took the idea with him when he went over to the BBC.

During the 1970s, game shows became more popular and started to replace expensive variety shows. As a result, many variety performers were recruited for game shows. The BBC, suffering poor ratings, decided to make its own game show. Bill Cotton, the BBC's Head of Light Entertainment, believed that Forsyth was best for the job. For years, The Generation Game was one of the strongest shows in the BBC's Saturday night line-up, and became the number-one game show on British television during the 1970s, regularly gaining over 21 million viewers. Its theme song "Life Is The Name Of The Game" was written and sung by Forsyth, and later released on record.

1978–1982: Larry Grayson era
In the mid-1970s London Weekend Television recruited Forsyth to host The Big Night on Saturdays. Alan Boyd, producer of The Generation Game at the time, remembers that there were many proposals as to who should take over, with Bill Cotton having a brief discussion with his favoured choice Cilla Black, who would not consider the move; other names mentioned included Jimmy Tarbuck and Kenneth Williams. However, he felt he did not want the new programme to be compared to Forsyth's Generation Game, so he cast Larry Grayson, with a new theme tune, which incorporated Grayson's "shut that door" catchphrase. There was also new scenery, and a new co-host, Isla St Clair. It worked, as The Big Night failed to beat The Generation Game in viewing figures and was off the air within three months.

The show reached its peak under Grayson. It attracted an audience of 25 million on one occasion, when a strike blacked out the ITV network.. Grayson's apparent incompetence and inability to remember what was going on was carefully contrived. In 1980 a junior version was considered, to be titled The Younger Generation Game, with two young siblings of different ages in place of older contestants. It was not confirmed whether Grayson would have hosted this proposed spin-off version, and it ultimately was never commissioned.

Cancellation
By the early 1980s The Generation Game was being beaten by ITV's Game for a Laugh. The show continued through to the end of 1981, but shortly after a highlights episode from the last series aired on 3 January 1982, Grayson decided to quit whilst the show was still popular. The BBC approached Jimmy Tarbuck to present the show but he turned it down. The show was later cancelled.

1990–2002 revival: Second Bruce Forsyth era and Jim Davidson
The Generation Game returned in 1990 with the original host, Bruce Forsyth, who after moving to ITV in 1995 was replaced by Jim Davidson. This incarnation ended in 2002 after again being beaten by ITV, this time by Pop Idol. Davidson had announced in March that he was quitting the show. The series ended the following month.

2003–2005: Paul O'Grady pilots and Graham Norton special
The BBC were planning on reviving the show with Paul O'Grady as its new presenter in 2004. Filming two non-broadcast pilot episodes in 2003, both O'Grady and the production team were unhappy with the result, with O'Grady leaving the project. Graham Norton hosted a one-off special at Christmas 2005 featuring celebrity contestants Kelly Holmes, Davina McCall, Rupert Grint and James Fleet; this was titled Generation Fame.

2007 retrospective
The Generation Game returned in 2007 under the title Brucie's Generation Game: Now and Then broadcast on UKTV Gold. This version was a retrospective of earlier editions, similar to the digital channel's Wogan and Jim'll Fix It revivals around the same time.

2011: David Walliams's 24 Hour Panel People
In 2011, a version of the show featured as part of David Walliams's 24 Hour Panel People, a charity marathon of game shows for Comic Relief. David Walliams competed with his mother Kathleen. The other team consisted of Miranda Hart and Patricia Hodge, who play mother and daughter in the sitcom Miranda. Vernon Kay presented the episode.

2014–2015: Miranda Hart discussions
On 20 April 2014, it was announced that comedian Miranda Hart (who appeared on the 2011 charity special) was in "early talks" with the BBC about hosting a revived version of the show. A pilot episode was filmed before Christmas that year but the controller of the channel, Charlotte Moore, revealed in August 2015 that the project was "very much on hold" due to Hart wanting to concentrate on her acting and writing career.

2017–2018: Mel and Sue
On 11 May 2017, it was reported that Mel and Sue were linked to host a reboot for the BBC as part of a package for not staying with The Great British Bake Off after its move to Channel 4. On 23 July 2017, it was confirmed that Mel and Sue would host. However, on 7 February 2018, two episodes instead of the planned four were confirmed, with the BBC saying "During the production process it's not unusual for a new series to change length as the format evolves".

The first episode aired on BBC One on 1 April 2018. It received generally poor reviews from TV critics. Gerard O'Donovan from The Telegraph gave it one star, writing: "...There's little to say other than that it was a shameless carbon copy of memorable moments from The Generation Game of the 1970s or 80s." Carol Midgley of The Times gave it two stars, saying: "It needs to relax and dial down the gush. Brucie made it look so easy. Didn't he do well?" The i Paper's Jeff Robinson said the show "felt forced and scripted, another territory for the Mel and Sue brand to colonise post-Bake Off rather than an original updating of an old format." Sam Wollaston of The Guardian was more positive, giving it three stars and writing: "Somehow, it manages to be both a little bit glorious and groansome to the max at the same time."

Catchphrases
The show introduced a number of catchphrases, including Bruce Forsyth's "Didn't he/she/they do well?", "Let's meet the eight who are going to generate" and "Let's have a look at the old scoreboard". Later, when the show was revived, Forsyth's assistant was Rosemarie Ford, so the catchphrase was amended to "What's on the board, Miss Ford?" (originally "What have they scored, Miss Ford?"). Forsyth always opened the show with "Good evening Ladies Gentlemen and Children welcome to the Generation Game, it's Nice to see you, to see you ..." to which the audience would shout "Nice!", a catchphrase that Forsyth retained in his later television appearances. Others included "Good game, good game," "I hope you're playing this at home," and "Give us a twirl," which was said to hostess Anthea Redfern to show off her dress.

Grayson supplied his own catchphrases, including "Shut that door!", "What a gay day!" and "Seems like a nice boy!" Scores were preceded by "What are the scores on the doors?" to which St Clair would reply "The names in the frames say..." before announcing them. After the conveyor belt finale, Grayson would say "What a lot you've got... you have got a lot!" but he abandoned this after his second season as it did not register with the public. Grayson and St Clair apparently had a strong bond; Grayson always introduced her at the start of each show as "my lovely Isla" and "my favourite girl, my Saturday girl." She once referred to them as being "like a couple of naughty sisters."

Jim Davidson would later present but no real catchphrases were used; however, he made a running gag acknowledging this and tried out several 'potential catchphrases'.

Hostesses
Each host of The Generation Game was joined by a female hostess, who brought the contestants on stage, handed out the prizes and often joined in the games. The first was Anthea Redfern, who began an affair with host Forsyth and married him during the series' run. When she was absent on maternity leave, actress Jenny Lee Wright stood in for a number of shows. Isla St. Clair was Grayson's hostess throughout his tenure on the show. Rosemarie Ford supported Forsyth on his second stint as host. Sally Meen, Melanie Stace and Lea Kristensen were Davidson's hostesses.

Board games
In 1975, Strawberry Fayre and Denys Fisher published a board game (simply called Generation Game with host Bruce Forsyth on the cover) featuring a three-dimensional diorama of the set, a working countdown clock and the famous sliding doors.

In 1990, Rainbow Games published another board game (only this time as Bruce Forsyth's Generation Game still with Forsyth on the cover).

Books
In 1992, a book called Bruce Forsyth's Generation Game Book: Games, Quizzes, and D-I-Y (Do It Yourself) Fun for All the Family was published by Vermillion.

International versions
In addition to the original Dutch version and long-running British version, Rudi Carrell hosted the German version Am laufenden Band from 1974 to 1979 on Das Erste. There was also a Swedish version, Tjocka Släkten, presented by Lasse Berghagen and Inga Gill from 1990 to 1991. In 2008 a South African version of the show was made, hosted by comedian Barry Hilton together with actress/presenter Cindy Nkabinde on channel SABC 2.

title: The Generation Game


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Lake Garda

Lake Garda (Lago di Garda,, or (Lago) Benaco, ; Lach de Garda; Ƚago de Garda) is the largest lake in Italy. It is a popular holiday location in northern Italy, between Brescia and Milan to the west, and Verona and Venice to the east. The lake cuts into the edge of the Italian Alps, particularly the Alpine sub-ranges of the Garda Mountains and the Brenta Group. Glaciers formed this alpine region at the end of the last ice age. The lake and its shoreline are divided between the provinces of Brescia (to the south-west), Verona (south-east) and Trentino (north).

Etymology
In Roman times the lake was known as Benacus and by some it was revered as god Benacus, the personification of the lake, sometimes associated with the cult of Neptune. Today it is better known as Lake Garda, a toponym of Germanic origin attested since the Middle Ages and deriving from that of the homonymous town on the Veronese shore of the lake, which, together with another famous locality of the lake, Gardone Riviera, and others less known – such as Gàrdola, Gardoncino, Gardoni, Guàrdola and Le Garde – testifies the Germanic presence in the area that goes from the 6th to the 8th century CE, in particular, the Lombard one. The name Garda is evolved from the Germanic word warda, meaning "place of guard", "place of observation" or "place of safety".

The classic toponym of the lake, or Benācus lacus (Benaco), is almost certainly of Celtic origin, therefore prior to romanization, and should derive from bennacus, comparable with the Irish bennach, which means "horned". The term may derive from the many promontories of the lake.

Morphology and hydrography
The northern part of the lake is located in a depression that insinuates itself inside the Alps, while the southern part occupies an area of the upper Pianura Padana. The shape is typical of a moraine valley, probably having been formed under the action of a Paleolithic glacier. Although traces of the glacier's actions are evident today, in more recent years it has been hypothesised that the glacier occupied a previously existing depression, created by stream erosion 5 to 6 million years ago.

A characteristic of Garda is the limited size of the hydrographic basin (2,290 km2) compared to the lake surface: at a length of 52 km of the lake corresponds the 95 km of the basin, while the respective widths are 16 km and 42 km. The eastern watershed of the Benacense basin has a direction parallel to the axis of the lake, while the western one has a more sinuous course. Within the basin, the major peaks are Presanella (3,556 m) and Adamello (3,554 m). Morphologically, the Garda hydrographic basin can be divided into four areas: the plain of about 200 km2, the lake surface of about 370 km2, the western portion of about 500 km² and the eastern one of approximately 1,040 km2.

To the south of Lake Garda, between Brescia, Mantua and Verona, a large morainic amphitheatre develops: a succession of hilly circles with small flat areas interposed, in some cases marshy, originated thanks to the transport and storage action of the great Garda glacier. These morainic deposits were formed during the glaciations Günz, Mindel, Riss and Würm: very limited morainic deposits are attributed to the two oldest, Günz and Mindel, while the outer morainic circles are attributed to the Riss glaciation and the inner ones to the Würm glaciation. The morphology of the hills is gentle and with delicate lines; from the highest points, it is possible to perceive the relationships that link the hills to the mountains as well as the circular amphitheatre shape of the hills, which seem to embrace the southern part of the lake.

The main tributary of Lake Garda is the Sarca River, others include the Ponale River (fed by Lago di Ledro), the Varone/Magnone River (via the Cascate del Varone) and various streams from both mountainsides, while the only outlet is the Mincio River (79 m, at Peschiera). The subdivision is created by the presence of a fault submerged between Sirmione and Punta San Vigilio which is almost a natural barrier that hampers the homogenization between the water of the two zones.

If the water level of the Adige River is excessive, water is diverted to the lake through the Mori-Torbole tunnel.

Geology
The Lake Garda area is considered one of the most seismic in Italy. The oldest known earthquake that struck the Garda region seems to have occurred in 243 (or perhaps 245): it was so disastrous that the city of Benaco, located where Toscolano Maderno stands today, suddenly disappeared. The disappearance of the town is probably due to the cracking and landslide of the mountain above Toscolano, which caused the flooding of a small lake enclosed by the mountains, whose waters submerged the populous town.

Other earthquakes, more or less intense, followed one another periodically: in 793, when according to the chroniclers it caused great calamities, especially in the Baldo area; in 1457, during which a mountain above Salò lowered; in 1703, when it caused the fall of numerous houses and caused many victims; in 1810, an earthquake particularly hit Malcesine where it caused a clouding of the waters and the formation of a crack 200 m long and 18 cm wide in the town square; in 1836, when the tremors caused some landslides in Mount Tomè, in the northernmost part of Monte Baldo, which in turn caused a strong eruption of water.

In 1866 a rather long period of seismic agitation began in the Baldo area, with earthquakes of varying intensity, tremors, shaking and other phenomena of lesser importance, which saw as the most important event the earthquake of 5 January 1892, which shook the entire Garda region with extraordinary violence, causing the fall of chimneys and walls.

Other earthquakes more recently hit Salò and its surroundings, in particular, the earthquake of 31 October 1901 caused widespread damage to buildings, some collapses and cracks in the ground, while another earthquake in 2004 caused damage to some buildings.

Islands
The lake has also numerous small islands and five main ones, the largest being Isola del Garda. Nearby to the south is San Biagio island, also known as the Isola dei Conigli ("island of the rabbits"). Both are offshore of San Felice del Benaco, on the lake's western side. The three other main islands are Isola dell'Olivo, Isola di Sogno, and Isola di Trimelone, all farther north near the eastern side.

Climate
The particularly mild climate favours the growth of some hardy Mediterranean plants, including the olive tree, parasol pine, mediterranean cypress, chinese windmill palm and Canary Island Date Palm. Some hardy citrus trees, such as hardy lemons and satsuma can also be found, which are extremely rare at this latitude (46° North). In ancient times, poets like Catullus wrote about "Lacus Benacus" with its mild climate vivified by the winds. The lake is oriented from north to south towards the Po Valley, so many winds typical of the lake are the result of a difference between lower and higher altitude temperatures. Due to this, winds are generated that descend from the mountains to the plains in the morning and go back to the mountains in the afternoon. The bottleneck formed by the lake basin affects the timing of the winds, many of which happen on a regular daily basis. The winds are all named, most in regional Italian dialect so a single wind may have different names.

Fauna and flora
Lake Garda is rich in biodiversity. Salmo carpio, also known as the carpione (carpione del Garda or Lake Garda carpione ) is a rare salmonid fish endemic to Lake Garda. It has been introduced to a number of other lakes in Italy and elsewhere but unsuccessfully in all cases. The population in Lake Garda has been strongly declining, and is considered critically endangered (IUCN 3.1). The main threats are due to overfishing, pollution and possibly competition from introduced species such as Coregonus and other Salmonidae.

Adult lake trout outside the mating season are silvery with very few black spots on the body and almost none on the head. During the mating season, some males develop a dark mottled body colouration. Garda lake trout reach a length of up to 50 cm. They live primarily in depths of 100 to 200 m. They feed on zooplankton and bottom-dwelling crustaceans in summer. Males and females reach sexual maturity at two or three years. The mating takes place every one to two years. The spawning takes place in 50 to 300 m depth in the vicinity of underwater springs. The maximum age is five years.

Areas around Lake Garda, inhabited since prehistoric times, are an environment of great naturalistic value, with vegetation typical of the Mediterranean climate such as olive trees, vines, lemon trees, agave and other plants, which thrive thanks to the microclimate created by the Garda basin, which makes winter particularly mild. During the spring wildflowers such as primroses, iris, violets and red lilies are born, while in summer some bloom varieties of wild orchids. Thanks to the presence of protected areas, hares and small wild mammals, water birds and birds of prey survive, while ponds and ditches are populated by pike, carp and eels. The herds of cattle, horses and other domestic animals give a bucolic aspect to the hilly landscape.

History
Traces of human presence around the lake have been found related to the Middle Paleolithic, in particular flint tools, but only above certain altitudes, as at lower altitudes, the actions of the glaciers have cancelled all the clues that could have proved the presence of man. There are some signs of encampments from Upper Paleolithic, in particular on the slopes of Monte Baldo and Stivo. In the Neolithic the populations that inhabited the lake came into contact with the square-mouthed vases culture, as evidenced by the objects accompanying some tombs from this period found near Arco.

Bronze and Iron ages
The greatest evidence of human presence in prehistoric times dates back to the Bronze Age, when numerous aggregates of stilt houses arose in the lower lake before being abandoned during the Iron Age in favour of more strategic points. Lake Garda was a meeting point between the populations of Reti and Veneti, whose presence is testified in particular by the necropolis of Garda, as well as that of the Etruscans who came to trade in these areas. Also plausible is the presence of the Cenomani, who would have settled in the area between Brescia and the lake around the 6th century BC, leaving their traces mostly in the Lombard toponymy.

Roman times
The integration between Romans and Cenomani, who controlled the Garda area, probably began in 225 BC, when there was a treaty of alliance between Cenomani, Veneti and Romans, even if the actual Romanization of the territory took place between the 2nd and 1st centuries BC. In 89 BC the rights of Latin cities were granted to the Garda areas by the will of the Roman consul Gnaeus Pompeius Strabo, while forty years later Roman citizenship was finally granted to Brixia (whose countryside included the western and northern banks of the Benaco) and Verona (which instead included the eastern shore). During the 1st century AD many roads were built, such as the via Gallica, which connected Verona to Milan passing through Peschiera (the ancient Arilica), and the via Claudia Augusta, which connected the plain with the Resia pass and therefore the northernmost territories, as well as some minor roads that connected the Adige valley with the Garda. Two pagi were also established: pagus Benacenses on Brescia and pagus Claudienses on Verona.

In 268 AD the Battle of Lake Benacus was fought between the army of the Roman Empire, commanded by the future emperor Claudius Gothicus, and the German federation of the Alamanni. The overwhelming victory obtained by the Romans allowed the expulsion of Alemanni from northern Italy, due to the very serious losses they suffered during the battle.

The Roman presence is amply testified also by settlements, villas (in particular the notes Grottoes of Catullus), by the remains of centuriation still visible today, by the remains of sanctuaries, tombstones and epigraphic testimonies.

Middle Ages
In the Middle Ages Lake Garda was described by Dante in his Divine Comedy:

After the collapse of the Roman Empire, the Garda region witnessed the passage of numerous Germanic populations, but the first one that settled there, after a long migration, was that of the Lombards. Their testimonies are mostly present along the southern and eastern shores, preferred to other areas due to their strategic importance: from here it was possible to control both the waterways of Garda and Mincio, and the Adige valley. During the Lombard hegemony, there was a first administrative reorganization, as well as the definitive Christianization of the area, begun in the previous centuries by Vigilius of Trent and Zeno of Verona. The lake remained on the border between three powerful Lombard duchies: Brescia, Verona and Trento.

The first documents that testify the presence of a Fines Gardenses, an entity with its own officials for the administration of justice, even if not autonomous with respect to the Count of Verona, date back to 825, while after the year 1000 county of Garda was established by the emperor Henry II. Starting from the 11th century, towns around the lake began to develop a differentiated policy compared to that of the major centres of influence – Brescia, Verona and Trento – and this greater autonomy meant that many centres became free communities. These possessed comfortable economic conditions compared to the inland countries and a strong social awareness and sense of community.

In the 13th century, however, the Signoria Scaligera was established and it soon subdued the eastern shore of the lake. The Scaliger built numerous defensive constructions, in particular, they built the castles of Sirmione, Malcesine and Riva, reinforced the port structures of Lazise and Torri del Benaco, and built a great defense system called Serraglio, the only one of its kind in Italy. This fortified system, completed by Cangrande II in 1355, included isolated castles in Ponti sul Mincio and Monzambano, serious continuous and uninterrupted castles and towers connected by defensive walls starting from the fortress of Valeggio sul Mincio and then continuing up to Nogarole Rocca. The Seraglio remained practically intact until the mid-19th century when it was partially dismantled.

Early modern history
In 1387, following the defeat of Antonio della Scala, the whole Garda area was subjected to the Visconti; as early as 1405 the eastern shore passed into the hands of the Republic of Venice, while the western shore remained afflicted by the struggles between Guelphs and Ghibellines. In 1426 the Visconti lost Brescia and the western shore of the lake, which thus passed into the hands of Venice: gathered under the flag of the Republic of Venice, the 34 Benacense municipalities obtained ample autonomy. The war returned in 1438, due to the struggle between Venice and Milan: an exceptional event, remembered with the name of Galeas per montes, was the passage of a fleet composed of six galleys and twenty-five ships on the slopes of Monte Baldo, pulled by 2,000 oxen. This fleet sailed on Adige and almost reached Rovereto, from where it was transported to Lake Garda by land through the valley of Lake Loppio. The fleet was then used to counter the Milanese one and had its greatest success in a battle at Riva del Garda, which was followed by the capitulation of the city.

In 1508 the League of Cambrai was formed against the Serenissima: Venice strengthened the castles of its mainland domains, including those of Salò and Padenghe, and sent several galleys to the lake, as well as having new ones built directly on Lake Garda. During the war the Venetians lost part of their domains which were however recovered in 1512. In 1516 emperor Maximilian I came to Italy and the lake returned to German hands again, allowing the Serenissima to recover the lost territories.

In 1796 the territories of the Serenissima were involved in the Napoleonic wars: at the end of May, the French advanced to the lake and defeated the Austrians at Borghetto sul Mincio, conquering Peschiera. At the end of July, the French were defeated and had to retreat beyond Salò, which was then occupied by the Austrians. Numerous clashes took place between the adversaries on the battlefield of Lake Garda. In 1797 the French occupied Mantua, while Brescia valleys and towns on the lake rose up against the Napoleonic forces, even if the Republic of Venice maintained its neutral status and did not send aid to rescue. The Veronese, on the other hand, autonomously organized expeditions against the centres occupied by the French, but were defeated and forced to retreat to Verona, where on 17 April the anti-French insurrections called "Pasque Veronesi" (Pasque Veronesi) began. ". On 17 October the Treaty of Campoformio was signed: the southwestern shores went to the French, while the north-eastern ones went to the Austrians. In 1799 the war continued until the following year the lake returned to French hands: it became part of the Cisalpine Republic (later transformed into Italian Republic and then again in Kingdom of Italy, always under French control.

In 1815 following the definitive defeat of Napoleon Bonaparte, during the Congress of Vienna it was decided to create the Kingdom of Lombardy–Venetia: in this way, the whole Garda region returned to Austrian hands.

Later modern and contemporary history
The First Italian War of Independence saw an initial slow advance of the Piedmontese army towards the lake: at the news of its approach, Salò rebelled against the Austrians, several soldiers were taken prisoner and the Austrian insignia demolished. During the events also Riva del Garda and several towns on the Veronese side rose up. The Austrian army was forced to retreat to the Mincio line due to the advance of the Piedmontese troops and on 4 April the Austrians were driven out of Lonato and Desenzano, while the Piedmontese attempt to conquer Peschiera was unsuccessful. After the Piedmontese defeat of Custoza the pre-war status quo was restored. In 1859 the Second War of Independence began; on 18 June the Hunters of the Alps managed to enter Salò, from where Giuseppe Garibaldi wanted to leave to continue the advance towards Veneto crossing the lake with some boats, but new orders forced him to move the troops in the Brescia valleys. However, the Italian troops managed to sink an Austrian steamship before leaving Salò. Shortly after the battle of Solferino and San Martino was won by the Franco-Savoyards and Peschiera was besieged. With the armistice of Villafranca the war was put to an end: Garda returned to be a land border, on this occasion between Italians and Austrians. During the Third War of Independence Garibaldi returned to Salò again and from there he invaded Trentino. Meanwhile, the Austrians repeatedly bombed Gargnano and tried to impose their dominance. Despite the humiliating Italian defeat, in 1866 Veneto was finally handed over to the Kingdom of Italy, except for the northern part of the lake which still remained under Austrian control.

During the First World War towns on Lake Garda were bombed several times. On 23 July 1915, the first aerial bombardment took place in the area, when Riva del Garda was hit. The steamers of the lake were requisitioned by the Italian army and were re-equipped as warships. The following year some guns and artillery batteries were installed, but on 20 February 1916, Riva was hit again. The following day three Austrian planes bombed Desenzano, while on 27 February bombs fell in Nago and Torbole. In 1918 Riva was bombed again. Later Limone and, once again, Riva were targeted, but with the end of the war, Trentino also passed into Italian hands.

In the period between the two wars the poet Gabriele D'Annunzio settled in Gardone Riviera, where the "Vittoriale degli Italiani", his residence and now a museum, would later be built.

Until 1943 the events of Second World War did not particularly affect the lake region, but following the birth of the Italian Social Republic the German command settled in Limone and, on 10 October, that of Benito Mussolini in Gargnano. The Ministry of Defense was located in Desenzano; the Ministry of Foreign Affairs, the Ministry of Popular Culture and the press agencies settled in Salò, which became the capital of the newborn Fascist Italy. At the end, Mussolini was strung up on a lamppost in his Lake Garda enclave.

Fasano was the seat of the German embassy and Gardone of the Japanese one, while the Ministry of the Interior and the seat of the Republican Fascist Party (PFR) found accommodation in Maderno. The upper part of the lake was also occupied militarily by the Wehrmacht. In April 1945 the lake was freed by the Allies and later became part of the Republic of Italy. The award winning documentary film The Lost Mountaineers looks at the tragic events that happened in the last days of the war in northern Lake Garda.

Myth and Legend
According to the Greco-Roman mythology, the River Mincius was the child of the Lake Benacus.

In ancient German Sagas, Garda was home to Ortnit.

Towns and villages on the lake
Around Lake Garda there are 26 comuni, the most populated being Desenzano del Garda (29,179 inhabitants), followed by Arco (17,857) and Riva del Garda (17,518).

Tourism
Garda's economy is based on tourism. Back to Roman times, especially from the early imperial age, magnificent villas were present on the shores of the lake, conceived as places dedicated to otium, an activity actually reserved for the ruling classes. In particular Sirmione was a privileged place for the presence of sulphurous springs that allowed thermal use. Starting from the Renaissance the lake returned to be populated with noble villas.

Tourism in the modern conception of the term, however, developed from the end of the 19th century, even if it was still an élite tourism that concerned almost exclusively the north-western area of the lake. One of the first tourist resorts was Gardone Riviera, where the first small hotel was built. Expanded over time, it became one of the buildings that made up the luxurious Grand Hotel Gardone Riviera. In its vicinity other small hotels and villas slowly arose and, after the poet Gabriele D'Annunzio had the Vittoriale degli Italiani built here, the fame of the place grew further.

On the Veronese shore, tourism arrived much later, around the 1930s, when the current Strada Gardesana Orientale was built along the shores of the lake. With the arrival of tourists, "lakeside promenades" were planned. Since the 1950s tourism has undergone a sort of transformation: tourism with a long stay has been accompanied by "hit and run" tourism, with a short stop, just for the weekend or even for a few hours. The first is fed by tourists who want to spend their holidays on the lake, coming from different areas (in addition to Italians, numerous Germans, French, Swiss and Dutch), while the second is fed by those who live a short distance from the lake and who want to spend a few hours there. Both types of tourism have caused notable changes in the organization of the territory and the inhabited centres.

Furthermore, in the second half of the 20th century, a real entertainment industry was formed along Lake Garda as a series of parks were built. The most important is Gardaland, the biggest Italian theme park which hosts numerous tourist attractions.

Lake Garda is also a popular destination for sport tourism. Riva, Torbole and Campione are famous for winds that attract people who practice sail, windsurf and kiteboard. The | Centomiglia Regatta is also sailed there every year.

Ferries
Ship transport is provided by Navigazione Laghi. A daily ferry service connects major towns on the eastern and western shores of Lake Garda. The service runs from Desenzano del Garda to Riva del Garda, via Peschiera del Garda, Salò and Malcesine.

Railway
The region can be reached directly via the Milan-Venice railway, with Desenzano-Sirmione and Peschiera railway station.

Buses

Buses are faster alternatives to ferry services. On the eastern coast, ATV (Verona Transport Company) provides at least five daily bus routes between Verona and Garda, with one route extending to Riva del Garda. Trentino Transporti provides daily bus routes between Riva del Garda and Rovereto or Trento. On the western coast, SAIA (Brescia Mobilità) provides regular bus services between Desenzano del Garda, Salò, Gargnano and Brescia.

Highways
The lake is located at the centre of a crucial node between Brescia, Verona and Trento, and is therefore easily reachable via the transversal infrastructures of the Po Valley and those of the Brenner-Rome axis:

Roads
Lake Garda is also served by a road network that runs along the entire lake and is made up of the following infrastructures:
 * Strada Statale 11 Italia.svg State Highway 11 Padana Superiore, from Desenzano del Garda to Peschiera del Garda
 * Strada Statale 45bis Italia.svg State Highway 45bis Gardesana Occidentale, from Salò to Riva del Garda
 * Strada Statale 249 Italia.svg State Highway 249 Gardesana Orientale, from Peschiera del Garda to Riva del Garda
 * Strada Statale 572 Italia.svg State Highway 572 di Salò, from Desenzano del Garda to Salò

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Lake Garda


text:
Talk:Abecedarian

I question the entire veracity of this article
As per the below commenter as well, I don't think this article reflects historical accuracy. The only references are A)dictionaries/thesauruses/etc. which establish only that this word has been used in the English language with this meaning and B)the Catholic Encyclopedia from no later than 1913. It is notable that this entry does not even appear in the current version of the Catholic Encyclopedia. It seems very likely that the story presented herein is not actually true, or at the very least that there is no reliable historical evidence that these events ever occurred or this sect ever existed as it is described. Additionally, the 1907 and 1913 versions of the Catholic encyclopedia give different other Anabaptist leaders as the supposed doctor who gave up his title of Doctor to follow this doctrine. This seems pretty clearly a lie, albeit probably a historical one and not a modern wiki forgery. Mathlaura (talk) 11:37, 30 December 2014 (UTC)

Source: An unnamed encyclopedia from a project that puts out-of-copyright texts into the public domain. This is from a *very* old source, and reflects the thinking of the turn of the last century. -- BryceHarrington

It does read as rather fanciful. Nonetheless, O.E.D. provides some more reputable sources: "hist. With capital initial. A member of a sect of Anabaptists founded in Germany in the first half of the 16th cent. under the leadership of Nicholas Storch (died after 1536), which opposed all forms of learning, including knowledge of the alphabet." "Abecedarians,—a sect of Anabaptists who pretended that, in order to salvation, a person must be unqualified either to read or write, and must be ignorant of the letters of the alphabet; from which circumstance their name originates." "In early sixteenth-century Zurich a sect of Anabaptists called Abecedarians claimed to have direct inspiration from God and maintained that human learning was an impediment to divine illumination."

SXibolet (talk) 19:16, 23 July 2019 (UTC)
 * I came to the article after encountering two references within a few days. Widely separated and completely unrelated books, and I cannot remember any previous references (though I have previously read a number of books from Umberto Eco, who wrote one of the books). Having said that, I didn't get much enlightenment from the Article... Shanen (talk) 05:57, 7 September 2022 (UTC)

Affected vs. Effected
The correct verb here is "effected," as it refers to a bringing about of something, rather than as an alteration or influence upon something.

Shouldn't this be merged with (or at least linked to) Zwickau prophets?--88.73.5.203 (talk) 18:02, 21 July 2012 (UTC)

 * Actually, affect is perfectly correct here. It is used in the sense of claim, pretend and the implication is that their 'absolute disdain for all human knowledge' was bogus, not genuine. (They didn't bring about this disdain). Compare with affected and affectation. This is arguably POV, but linguistically correct. Norvo (talk) 22:19, 16 March 2014 (UTC)

Merge with Zwickau prophets
Besides the dubiousness already expressed above, from what I can gather in older sources, "Abcedarian" seens just an epithet for the Zwickau prophets. (e.g. 1, 2, 3, 4, etc.) rather than a distinct sect in itself. This article seems superfluous and should be merged. Walrasiad (talk) 03:19, 29 December 2020 (UTC)

Agree. 216.8.188.31 (talk) 20:47, 4 January 2021 (UTC)

Please delete the pic that I have uploaded on wikipedia
Respected sir/mam, I have uploaded the pic The reference of the pic is shared i want it to get deleted as soon as possible , This pic is own by me and please delete these pic as soon as possible from Wikipedia licence Minaro123 (talk) 09:29, 22 October 2022 (UTC)

title: Talk:Abecedarian


text:
List of dragons in popular culture

This is a list of dragons in popular culture. Dragons in some form are nearly universal across cultures and as such have become a staple of modern popular culture, especially in the fantasy genre.

Dragons in fiction
This list of dragons in fiction is a list of draconic characters that appear in various works of fiction. It is limited to well-referenced examples of dragons in literature, comics, film, television, animation and video games.

Dragons in literature
Western literature tends either to affirm or pointedly subvert the traditional portrait of dragons from Western myth and folklore, as evil and greedy.

 * Author name legend

Dragons in comics
Dragons appear in various manga and american comics, in the form of comic books, comic strips and webcomics.

Dragons in film
Dragons have been portrayed in film and television in many different forms. They may terrorize human towns, or save human lives, even taking the role of passionate protectors.

Dragons in video games
Dragons appear in numerous games with fictional setting as bosses, final bosses, and enemies, as well as player characters, companions, units, and supporting characters.

Dragons in online audiovisual media

 * The Strong Bad Emails (flash cartoons) on the Homestar Runner website feature a dragon named Trogdor the Burninator.
 * The Great Dragon of Bleecker Street is a character featured in Dimension 20's The Unsleeping City.

Dragons in radio

 * Trorg, the Last Amber Dragon, and the blue sock-stealing dragons in Hordes of the Things

Dragons in songs

 * Albi, from the Flight of the Conchords song "Albi the Racist Dragon"
 * "Puff, the Magic Dragon" is best known from the hit single by Peter, Paul and Mary, but has been performed by countless other artists. "Puff the Magic Dragon" was first a poem by Leonard Lipton and adapted by Peter Yarrow. The poem tells of an ageless dragon who befriends a young boy, only to be abandoned as the boy ages and forgets him. This is sometimes suspected of being riddled with references to marijuana, though the authors have publicly ridiculed this notion. The dragon in the song is most likely a reference to children's imagination and innocence.
 * Tharos, from the Emerald Sword Saga, a collection of five albums by the symphonic metal band Rhapsody
 * The titular dragon in the song "The Dragon and Saint George" (2015) from Ten's release of the same name

Dragons in puppetry

 * Dirty Dragon from The BJ and Dirty Dragon Show and Gigglesnort Hotel
 * Scorch the Teenaged Dragon, Ronn Lucas' ventriloquism puppet
 * Delbert the Dragon, created by Jim Henson for La Choy commercials
 * Kukla from the children’s show Kukla, Fran and Ollie

Dragons in toys

 * Scorch, Slayer, Loong, Dragon, Legend, Magic in Beanie Baby
 * Megatron in Beast Wars becomes a bio-mechanical dragon after absorbing the essence of his ancestor.
 * Predaking and the Predacons in Transformers: Prime have robotic dragons as alternate forms.
 * Jinafire Long, the daughter of a Chinese dragon from Monster High

Dragons in theme parks and shows

 * Tradinno, the world's largest walking robot
 * Prezzemolo in Gardaland
 * Figment in Journey into Imagination with Figment
 * Danny in Happy Hollow Park & Zoo
 * The Dragon in Legoland
 * The 6 Dragons in Phantasialand
 * Coaster in Rye Playland

Dragons in sport

 * FC Porto, professional association football team from Portugal, nicknamed Os dragões and playing home matches at the Estádio do Dragão
 * Wales national association football team, presenting the Welsh Dragon (y Ddraig Goch) on its crest
 * San Francisco Dragons, field lacrosse team
 * Somerset County Cricket Club, one of the first-class cricket clubs in England
 * St. George Illawarra Dragons, Australian professional rugby league club
 * Barcelona Dragons, professional american football team playing in the ELF
 * Mario the Magnificent, Drexel Dragons mascot
 * Stuff the Magic Dragon, Orlando Magic mascot

Dragons in podcasts

 * Hiram McDaniels, a "literal five-headed dragon", and his sister Hadassah McDaniels from Welcome to Nightvale. Each head demonstrates differing personality traits and behaviors.
 * Cerulean Depths Seen from a Great Height (A.K.A. Ceri). A gargantuan sea dragon with a long name and a snobby teen attitude, from Spout Lore.
 * Mishka Beverly Paw Paw II, an energetic and rambunctious baby black dragon from Not Another D&D Podcast.

title: List of dragons in popular culture


text:
Talk:List of miscellaneous fictional animals

Comments from 2003-2004
What sort of fish is Nemo in Finding Nemo? -- Timwi 01:29 19 Jun 2003 (UTC) P.S. please avoid spoilers, I've yet to see it... thanks -- Timwi 01:31 19 Jun 2003 (UTC)

Wow, learnt something new today. A sponge is an animal. Thx Wiwaxia ~ender 2003-09-20 00:57:MST

Anyone got any information on TaoTao? (Panda) Mat-C 05:35, 26 Apr 2004 (UTC)

A clownfish. Also, the amount of fictional animals is infinite! Surely you jest!?
 * We have now decided to include only notable animals. I agree that this list is still potentially infinite, but at least it's more manageable. If you think the list should be deleted entirely then please visit WP:AfD. Frankly I think categories are a much better way to deal with a topic like this than a list. -Thibbs (talk) 13:41, 17 September 2010 (UTC)

Overall organization
I think that the organization of these fictional animals according to form of media is not the best. It is true that this is how the lists on other fictitious animals is organized, but structurally the form of subdivision used here is of a lesser order than a subdivision based on species (or genus, etc) of animal. If it were otherwise, I would expect articles on "list of fictional animals in video games" rather than "list of fictional dogs." Unless there are any reasons to keep things as they are currently, I will make the change to divide these animals by kind rather than by medium. This would also allow us the benefit of using main-tags. Any objections? -Thibbs (talk) 20:00, 25 February 2009 (UTC)

 * I agree. This combines a list of types of animal with a list of specific animals. (I think both are ridiculous, but I'm not going to win that argument.) 86.131.89.40 (talk) 00:17, 28 February 2009 (UTC)

Zoo Tycoon
Why the heck are there Zoo Tycoon animals here? They aren't fictitous! 78.148.111.226 (talk) 18:16, 20 February 2010 (UTC)

List of Fictional Weasels
This is a separate article & it has now been deleted due to lack of notability. Is this siome kind of sniping campaign against this larger article? Because itr makes nom sense to have weasels unrepresented when there are categories for sponges, molluscs, wombats - even a bloody pangolin for god s sake. What has anyone got against weasels fer Chrissakes? Now we see the naked mustelidophobia. Its the "Wind in the Willows" fiasco allover again!--Streona (talk) 14:57, 15 July 2010 (UTC)

I just cut out a lot of trivia
This article is in dreadful shape. I have removed all entries relating to speculative, imaginary, chimerical, legendary, etc. creatures based on User:Number36's argument that "Animals = Members of the taxonomic kingdom Animalia" and thus this article "List of fictional animals (other)" should cover only actual animals. For this reason I have also removed all robots, Pokémon, and creatures referred to as "something-likes" (e.g. Frank the shrewlike; or Jerry, a large llamalike). The article has also been tagged as suffering from lack of notability. To address this I have removed all entries referring to characters that are so minor in relation to the work they come from that they do not even have names. This includes animals like the spider that bit spiderman and all of the creatures from the vast Zoo Tycoon franchise. Referring to WP:LSC I think it is clear that we are in need of stricter inclusion criteria for this article. I would strongly favor only adding a new entry to this list if the subject of the entry can be linked as a stand-alone article or at least as a separate subsection of an article. I think this would go a long way to guarding this article from turning into nothing more than an indiscriminate collection of information. Does this sound like a good idea to everybody? -Thibbs (talk) 03:25, 5 September 2010 (UTC)
 * I have now begun adding "citation needed" tags to red-linked entries that I cannot immediately discard as non-notable. These entries are presumed non-notable because there is no article on them, however I think it is most prudent to request that citations be added to demonstrate notability for the time being until an article (or at least a subsection in another article) can be written on the topic. Cheers. -Thibbs (talk) 14:35, 5 September 2010 (UTC)

Well it's been a week now and although we have seen the addition of 43 new entries to this list in the last 7 days we have seen no attempts to find citations or article-work on the redlinked entries. I know a week isn't terribly long to wait for citations to emerge, however the notability problem this page faces is sufficiently grave that I think it works best at this point to simply remove all red-linked entries. Although I was willing to wait for a short period of time for citations to emerge covering the potentially non-notable entries, I don't think this policy should be followed in the future since this article is so given to non-notable bloating. I propose that in the future we should presume non-notability when no article on the character or subsection on the character exists. It is debatable whether links to subsections with names like "Characters from Cartoon X" should be considered sufficient. At present I have left these entries intact. If this proves unmanageable then I think we should go for a stricter inclusion criterion and require that the entries have articles associated or subsections with the character's name. Does this sound reasonable? -Thibbs (talk) 00:21, 13 September 2010 (UTC)
 * I've gone through the list again and have relinked all former links that failed to point to articles or subsectiosn about the character. If the character is notable enough to be listed on this list then the proof of this is that an article or a subsection exists on the character. This still leaves us with a hierarchy among the listed entries. From most notable to least:
 * Characters with articles devoted to them alone - e.g. Arthur Read
 * Characters with subsections devoted to them alone - e.g. Cerebus
 * Characters with subsections devoted to a class of characters of which they form a pseudo-subsection or are a major part - e.g. David L. Read
 * Of these three kinds of characters, the first category clearly has the presumption of notability as this is a requirement for stand-alone articles. The notability of the second category of characters is rather more debatable but at this point I'm willing to allow them to stay. The notability of the third category is quite suspect. If this article was to undergo another major de-bloating then I'd say that this is the first category to be removed.
 * The last project I want to undertake to repair the notability issues is to search through the redirects. Many of the redirects are malformed and they point to an article on the parent work from which the character comes when they should instead point to the subsection on the character itself. I will repair these and these entries should remain on the list as category 2 or 3 members (referring to the above hierarchy). For redirects that cannot be sublinked to a character or class of characters, however, they form a category 4 level of non-notability. I will list those entries here before removing them and then I think they should be removed. Cheers -Thibbs (talk) 13:37, 17 September 2010 (UTC)

I was able to repair 4 of these redirects and I was able to relink a few more non-character links to their appropriate subsections, however there were a number of redirects that I could not attach to an article or subsection on the character and I have removed these. Here I will list them all so that this decision can be more easily reviewed: Non-character redirects

Blue Aardvark

Pau amma

Archy (character)

Charlie Ant

Sredni Vashtar (character)

Ecco the Dolphin (character)

Rikki-Tikki-Tavi (character)

Ty the Tasmanian Tiger

Wendell T. Wolf All of these redirects actually point to the underlying work but not to the character member of this list ("List of fictional animals (other)"). Because there is an issue about whether or not the characters are notable and because these characters do not actually have articles or subsections devoted to them I think it's a fair presumption that they are not notable enough to support an independent article. -Thibbs (talk) 14:44, 19 September 2010 (UTC)

Reworking organization
I have just reorganized this list to repair the strangely inconsistent approach whereby subsections listing animal phyla (e.g. arthropoda) were given equivalent subcategorization as subsections listing animal species (e.g. Aarvarks). I have now recategorized it such that the first level of subcategorization covers phyla, the second level covers classes, the third level covers orders, and the fourth level covers all lower groupings (families, genera, and species). I have altered the subsection titles where I felt that the average reader might not be familiar with the meaning of the term. The hope is that this will protect against the unnecessary addition of duplicative categories by editors who have not actually reviewed the article but have only used the TOC. I have also altered the TOC depth to show orders as the deepest level. I hope this tidies things up a bit and gives it an objective categorization which will allow much greater consistency. -Thibbs (talk) 17:31, 19 September 2010 (UTC)
 * I just merged all subsections that differentiated down to the species level. I think it makes good sense for this article to descend no deeper than genus considering that the more specific "List of fictional... Animal-X" articles (e.g. List of fictional cats, List of fictional dogs, etc.) would be the place where species-level differentiation occurs. If a family or genus becomes too populous here I think that we should consider splitting it out and creating its own article. This is the only way to ensure that this article doesn't become fragmented into hundreds of subsections each holding only 2-3 members. -Thibbs (talk) 15:35, 22 September 2010 (UTC)

Shrews
Where the shrew? --Ljrfnfvfhe (talk) 12:27, 19 August 2012 (UTC)

Cetaceans and sirenians
I feel like the cetaceans should be merged with the ungulates. Cetaceans are also classified as ungulates, despite the fact that they, similarly to pachyderms, lack hooves. I would also consider doing a similar thing to the sirenians, since sirenians are also classified as ungulates (and by a greater extent, they are also classified as pachyderms). Since the sirenians do not have as many notable fictional characters of their numerous species as the cetaceans, they can be merged with another list one of three ways; A. either merge both the cetaceans and the sirenians into the ungulates list, B. merge the cetaceans into the general ungulates list, then merge the sirenians into the pachyderms list, or C. give the cetaceans their own article with a list of fictional cetaceans, then incorporate the sirenians into it to make it a list of fictional cetaceans and sireneans. --Uptherial (talk) 02:52, 3 December 2020 (UTC)


text:
Talk:Flag of the Republic of China

Requested move 31 October 2023

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: not moved. (closed by non-admin page mover) — Material  Works  13:09, 7 November 2023 (UTC)

– The proposed flags of Taiwan article should be moved to the Flag of Taiwan to include ROC era, Japanese colonial rule, Qing era, European rule and indigenous Taiwanese eras. This article should be focused on China's national flag from 1912 to 1949 during the mainland era. This is to avoid confusion between the 1912-1949 ROC and 1945 Taiwan under ROC. 142.113.183.163 (talk) 12:50, 31 October 2023 (UTC)
 * Flag of the Republic of China → Flag of China (1912–1949)
 * Proposed flags of Taiwan → Flag of Taiwan

 * It would make no sense to time-gate this article to 1912-1949, the same flag is in use today. CMD (talk) 13:07, 31 October 2023 (UTC)
 * It is. Taiwan has a big sovereignty problem, they're using the national flag of the defunct Republic of China, which the PRC and the international community views it a defunct state. Renaming this article to "Flag of China (1912–1949)" would be like the flag of South Africa during apartheid focusing solely on the mainland period. -142.113.183.163 (talk) 17:05, 31 October 2023 (UTC)

 * Oppose. The article covers both the flag of the pre-Taiwan republic and of Taiwan itself, which uses the same design. -- Necrothesp (talk) 13:36, 31 October 2023 (UTC)
 * Nay. The flags on Taiwan flown the Dutch, Spanish, Tunging, Qing, Japanese and ROC banners throughout its history. It has a sovereignty problem anyway. -142.113.183.163 (talk) 17:05, 31 October 2023 (UTC)

 * Strong oppose per above.  O.N.R.  (talk) 13:46, 31 October 2023 (UTC)
 * Oppose. This flag is the flag of Taiwan, and the current primary redirect is best. 162 etc. (talk) 16:20, 31 October 2023 (UTC)
 * Not exactly. This flag that Taiwan uses is actually the historical but defunct flag of the ROC. Changing the names would render the issue moot. -142.113.183.163 (talk) 17:05, 31 October 2023 (UTC)
 * The ROC is Taiwan. 162 etc. (talk) 19:22, 31 October 2023 (UTC)

 * Oppose. The purpose of the article name is to provide a, as far as possible, a non-confusing unique identifier for the design. As the ROC continues to exist (and in this case, perhaps used to indicate that it precedes its current reduced state of being just Taiwan), and "China" is used as the WP:COMMONNAME for the PRC, the current article name is quite satisfactory.
 * OP has a history of deliberately ignoring COMMONNAME or obtusely interpreting WP:NC-CN to create POV edits that - among other things - avoid/remove referring to the PRC as "China", and referring to the ROC/Taiwan as "China". Time to stop, OP. - RovingPersonalityConstruct (talk, contribs) 19:12, 31 October 2023 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
 * Oppose the proposed flag article is an article on proposed flags. I see no reason to expand the scope of that article. If you want to write a Flag of Taiwan article, without proposed flags, feel free to DRAFT:Flag of Taiwan --- 65.92.247.90 (talk) 11:44, 3 November 2023 (UTC)
 * Oppose per above, also see similar articles such as Government of the Republic of China and National Anthem of the Republic of China. -  C HAMPION  (talk) (contributions) (logs) 08:02, 4 November 2023 (UTC)

title: Talk:Flag of the Republic of China


text:
Naïve empiricism

Naïve empiricism is a term used in several ways in different fields.

In the philosophy of science, it is used by opponents to describe the position, associated with some logical positivists, that "knowledge can be clearly learnt through evaluation of the natural world and its substances, and, through empirical means, learn truths".

The term also is used to describe a particular methodology for literary analysis.

See also:
 * Empiricism
 * Falsifiability (especially, "Naïve falsification")

title: Naïve empiricism


text:
Corporation sole

A corporation sole is a legal entity consisting of a single ("sole") incorporated office, occupied by a single ("sole") natural person. This structure allows corporations (often religious corporations or Commonwealth governments) to pass without interruption from one officeholder to the next, giving positions legal continuity with subsequent officeholders having identical powers and possessions to their predecessors. A corporation sole is one of two types of corporation, the other being a corporation aggregate.

Ecclesiastical origins
Most corporations sole are church-related (for example, the archbishopric of Canterbury), although some political offices of the United Kingdom (e.g., many of the secretaries of state), Canada, and the United States are corporations sole.

The concept of corporation sole originated as a means for orderly transfer of ecclesiastical property, serving to keep the title within the denomination or religious society. In order to keep the religious property from being treated as the estate of the vicar of the church, the property was titled to the office of the corporation sole. In the case of the Catholic Church, ecclesiastical property is usually titled to the diocesan bishop, who serves in the office of the corporation sole.

The Catholic Church continues to use corporations sole in holding titles of property: as recently as 2002, it split a diocese in the US state of California into many smaller corporations sole and with each parish priest becoming his own corporation sole, thus limiting the diocese's liability for any sexual abuse or other wrongful activity in which the priest might engage. This is, however, not the case everywhere, and legal application varies. For instance, other U.S. jurisdictions have used corporations at multiple levels. In the jurisdictions of England and Wales, Scotland, Northern Ireland, and the Republic of Ireland, a Catholic bishop is not a corporation sole, and real property is held by way of land trusts, a tradition dating back to the suppression of Catholicism by Henry VIII during the English Reformation and the Penal Laws of Ireland.

The Church of Jesus Christ of Latter-day Saints uses the corporation sole form for its president, which is legally listed as "The Church of Jesus Christ of Latter-day Saints".

Iglesia ni Cristo was registered as corporation sole with the Insular Government of the Philippines in 1914 and with the People's Republic of China in 2014.

The corporation sole form can serve the needs of a religious organization by reducing its complexity to that of a single office and its holder, thereby eliminating the need for by-laws and a board of directors.

The Crown
Within most constitutional monarchies, notably the Commonwealth realms, the Crown is a nonstatutory corporation sole. Although conceptually speaking, the office and officeholder retain dual capacities in that they may act both in a corporate capacity (as monarch) and in an individual capacity (as a private person), they are inseparably fused in law; there is no legal distinction between the office and the individual person who holds it. The Crown (state) legally acts as a person when it enters into contracts and possesses property. As a person, the monarch (officeholder) may hold properties privately, distinct from property he or she possesses corporately, and may act as monarch separate from their personal acts. For example, Charles III as a natural person holds several separate offices, such as king of the United Kingdom, king of Canada, king of Australia, and the supreme governor of the Church of England, all of which are distinct corporations sole, even as he acts as a natural person in his private capacities separate and apart from his role filling these various offices (corporations). Likewise, the office of prime minister has use of certain properties and privileges, such as an official residence and decision-making powers, that remain with the office once the officeholder leaves, even as the officeholder may own property in a private capacity.

The sovereign's status as a corporation sole ensures that all references to the king, the queen, His Majesty, Her Majesty, and the Crown are synonymous, referring to exactly the same legal personality over time. While natural persons who serve as sovereign pass on, the sovereign never legally dies; thus the corporate nature of the office of sovereign ensures that the authority of the state continues uninterrupted. In other words, the sovereign is made a corporation sole to prevent the possibility of disruption or interregnum, thereby preserving the stability of the Crown (state). For this reason, at the moment of the demise of the sovereign, a successor is immediately and automatically in place.

As a corporation sole, the legal person of the sovereign is the personification of the state and consequently acts as a guarantor of the rule of law and the fount of all executive authority behind the state's institutions. As Australia and Canada have federal systems of government, the sovereign in these cases also possesses capacities as distinct corporation sole in right of each of the Australian states and Canadian provinces; for example, as His Majesty the King of Australia in Right of Queensland and His Majesty the King of Canada in Right of Alberta.

Secular application in the United States
Every state of the United States recognizes corporations sole under common law, and about a third of the states have specific statutes that stipulate the conditions under which that state recognizes the corporations sole that are filed with that state for acquiring, holding, and disposing of title for church and religious society property. Almost any religious society or church can qualify for filing as a corporation sole in these states. There can be no legal limitation to specific denominations, therefore a Buddhist temple or Jewish Community Center would qualify as quickly as a Christian church. Some states also recognize corporations sole for various other non-profit purposes including performing arts groups, scientific research groups, educational institutions, and cemetery societies.

Governmental

 * The Crown (sometimes regarded as a corporation aggregate)
 * Administrator of Japanese Property (no longer exists)
 * Auditor General for Wales
 * Chief Executive of Skills Funding
 * Children's Commissioner for England
 * Children's Commissioner for Wales
 * Commissioner for Older People for Northern Ireland
 * Commissioner of Police of the Metropolis
 * Comptroller and Auditor General
 * The Corporate Officer of the House of Commons, and the Corporate Officer of the House of Lords, two corporations established by the Parliamentary Corporate Bodies Act 1992
 * The Dawat-e-Hadiyah
 * Duke of Cornwall
 * Duke of Lancaster
 * Information Commissioner
 * Mayor (of London)'s Office for Policing and Crime
 * Judicial Appointments and Conduct Ombudsman
 * Lord Mayor of the City of London
 * Official Custodian for Charities
 * Immigration Services Commissioner
 * Police Ombudsman for Northern Ireland
 * Public Services Ombudsman for Wales
 * Public Trustee
 * Pubs Code Adjudicator
 * Receiver for the Metropolitan Police District (abolished)
 * Registrar General
 * many secretaries of state in the United Kingdom (various; most recently Foreign, Commonwealth and Development Affairs)
 * Solicitor for the affairs of the Duchy of Lancaster
 * Treasury Solicitor
 * London Fire Commissioner
 * Dai al-Mutlaq

In the Church of England

 * Archbishop of Canterbury
 * Archbishop of York
 * Bishops of the Church of England
 * Deans of the Church of England
 * Rectors and Team Rectors in the Church of England
 * Vicars in the Church of England

Examples of corporations sole in New Zealand

 * New Zealand Public Trustee
 * Māori Trustee, New Zealand

 * New Zealand's Office of the Privacy Commissioner

Examples of corporations sole elsewhere

 * The Diocese of Hong Kong
 * The Church of Jesus Christ of Latter-day Saints
 * Director of National Parks, Australian government
 * Governor General of Canada
 * Minister of the Government, Republic of Ireland
 * Public Trustee
 * The Archbishop of Manila
 * The Archbishop of New York
 * Office of the sovereign of Canada
 * The Catholic Bishop of Chicago, A Corporation Sole- The Archdiocese of Chicago
 * (Former) Administrator of the Southern Electricity Supply of New South Wales

title: Corporation sole


text:
Talk:Corporation sole

natural persons
Must these persons always be "natural persons"? PML.
 * Obviously, that's the (double) import of "sole" incorporation, a single person (at a time) and a single office . 72.228.177.92 (talk) 21:20, 19 February 2010 (UTC)

Doctor Who
Someone speaking in the House of Commons in 1998 gave a lovely description of this concept:
 * The Lord Chancellor is working on that, but he is rather like Dr. Who, because now and again he goes into the Tardis and comes out reborn and reinvigorated. The latest one popped out on 1 May and has promised that there will be a better fast-track procedure in the small claims court.

Marnanel 22:04, 27 Feb 2004 (UTC) >THIS IS REV-LEWIS REFERING OR RESPONDING TO THE CORPORATION-SOLE? THE WORD WITH THE QUESTION SIGN, HAS BEING NULLIFY PERTAINING TO THE "SOUL" OF HUMAN BEINGS OTHERWISE THIS FROM YOU DETERMINE AS A "SLICK" ONE.< (oswaldclewis@comcast.net)  — Preceding unsigned comment added by 50.140.103.117 (talk) 22:33, 29 August 2012 (UTC)

Tax exemption
I'm interested in how corporation sole in the Roman Catholic church relates to Sun Myung Moon tax case. Recalling the case from 20 years ago, I remember that the Unification Church defended Rev. Moon's holding of one million dollars in an interest-bearing account under his own name as being analogous to corporation sole; on that basis, they argued he should not have been held "criminally liable" for tax evasion (or "failing to report personal income") on the interest accrued during the 3 years he held the money before the Unification Church of America was incorporated as a 501c3. --Uncle Ed 14:11, 17 October 2006 (UTC)

Legal Jargon Needs Explanation
As I am not a lawyer, I cannot understand the wording of the first paragraph: "This allows a corporation (usually a religious corporation) to pass vertically in time from one office holder to the next successor-in-office, giving the position legal continuity with each subsequent office holder having identical powers to his predecessor."

"...to pass vertically"? Vertical means an upright angle, or in economics: "involving all stages from production to sale." I see no definition in my dictionary which would explain the meaning of the word in this sentence.

Secondly, I do not understand what "legal continuity" could mean. Does it mean a continual legal process which goes uninterrupted? There are many possibilities.

Looking at this statement objectively, I would take it to mean that the corporation itself is handed over to a new owner (sole.) Is this correct? The paragraph badly needs be better explained by someone who understands the subject. Neurolanis (talk) 20:18, 3 July 2011 (UTC)

 * I will work on fixing this, but for the sake of clarity in case anyone reads this, the "corporation sole" is akin to an "office" (office as in position, like political office). It's not exactly the same as a political office, as positions like Representative for Hawaii's First District don't come with additional personal rights (usually property rights) affiliated with the position. The position of ruling monarch over the United Kingdom, whether King or Queen, comes with ownership of a lot of property. Yet that property belongs the corporation. For example, the Queen would not be allowed to sell a piece of the Crown Jewels, even though she owns them personally. This is because they don't belong to her as a "natural person," or individual human being. It belongs to the King/Queen of the United Kingdom and can't be detached from that office. Were she to abdicate, she will lose all her royal property. Most importantly, the office has to be incorporated. Therefore, a position like the American Presidency is not a corporation sole per say, even though you could argue he temporarily "owns" the White House in that no one else can claim residency there other than himself and his family, and he cannot sell or rent out the White House, American Law does not classify the presidency as a corporation sole, so it isn't one. If this sounds like kind of an archaic legal category, that's because it is. It's largely used for royal and religious offices that were established in the Middle Ages.

 * So Neurolanis's last point is largely correct, in that the corporation is handed over, though it wouldn't quite make sense to call the new person an owner. A holder is better, in line with "holding office," as they don't own the corporation and lack the rights that come with ownership.

 * The vertical pass is chronological as it passes from one office holder to the next. The clearest example of this would be the office of the King or Queen of the United Kingdom (though this applies to most monarchies in most cases). When the ruling King or Queen of the United Kingdom dies, the "office" passes to his or her heir. So when George VI died, his daughter Elizabeth inherited his office and became Queen Elizabeth. When she passes away, Prince Charles will inherit the office and become King Charles (though his royal name may or may not actually become King Charles, as you're allowed to chose your royal name. George VI's birth name was Albert).

 * And this is where "legal continuity" comes in to play. There will never not be a King or Queen of England. When the reigning monarch dies, the office doesn't die; a new body is attached to the corporation sole without any interruption of legal power or need to reincorporate. Though the new King or Queen has a coronation, there is no need to re-establish that the King of the United Kingdom is a thing that comes with certain rights and powers. In that sense, it's like the King never died in a way. This is because when the King dies, his body dies, but not the corporation sole of the British King. Instead, he is replaced. This is called "the King's two bodies," and is the most famous example of the mechanics of a corporation sole. JapanOfGreenGables (talk)) 06:12, 24 June 2020 (UTC)

vertically in time
This does not make sense. — Preceding unsigned comment added by 109.144.226.103 (talk) 17:45, 28 April 2012 (UTC)

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Tax Free villages
I was told in a Permaculture course, Corp Sole can be used in an autonomous village settlement. Commonwealth cooperative assets have a sales tax but the community would be tax free.

I cant find any thing on this agreement for future micro grid circular economies using renewable resources for cooperative assets. Any help would be greatly appreciated. www.ecosutra.com — Preceding unsigned comment added by Ecosutra (talk • contribs) 07:06, 12 April 2022 (UTC)

title: Talk:Corporation sole


text:
T-bone steak

The T-bone and porterhouse are steaks of beef cut from the short loin (called the sirloin in Commonwealth countries and Ireland). Both steaks include a T-shaped lumbar vertebra with sections of abdominal internal oblique muscle on each side. Porterhouse steaks are cut from the rear end of the short loin and thus include more tenderloin steak, along with (on the other side of the bone) a large strip steak. T-bone steaks are cut closer to the front, and contain a smaller section of tenderloin. The smaller portion of a T-bone, when sold alone, is known as a filet mignon (called fillet steak in Commonwealth countries and Ireland), especially if cut from the small forward end of the tenderloin.

Experts differ about how large the tenderloin must be to differentiate T-bone steak from porterhouse. The United States Department of Agriculture's Institutional Meat Purchase Specifications state that the tenderloin of a porterhouse must be at least 1.25 in wide at its widest, while that of a T-bone must be at least 0.5 in wide.

Owing to their large size, and as they contain meat from two of the most prized cuts of beef (the short loin and the tenderloin), T-bone steaks are generally considered one of the highest quality steaks, and prices at steakhouses are accordingly high. Porterhouse steaks are even more highly valued owing to their larger tenderloin.

In British usage, followed in the Commonwealth countries, "porterhouse" often means a British sirloin steak (i.e. US strip steak) on the bone, i.e. without the tenderloin on the other side of T-bone. Some British on-line butchers also offer American style porterhouse steaks.

In New Zealand and Australia, a porterhouse is sirloin steak (strip steak in USA) off the bone.

The earliest mention of the term "porterhouse steak" in a newspaper appears to have been in a letter written by Thurlow Weed that appeared in the Hartford Courant on August 9, 1843, but the following year (August 24, 1844) it also appeared in a list of food prices in The New York Herald, and it appeared regularly in newspapers after that.

Anatomy of the T-bone
To cut a T-bone from butchered cattle, a lumbar vertebra is sawn in half through the vertebral column. The downward prong of the 'T' is a transverse process of the vertebra, and the flesh surrounding it is the spinal muscles. The small semicircle at the top of the 'T' is half of the vertebral foramen.

Preparation
T-bone and porterhouse steaks are suited to fast, dry heat cooking methods, such as grilling or broiling. Since they contain a small amount of collagen relative to other cuts, longer cooking times are not necessary to tenderize the meat. There is some contention as to whether the bone conducts heat within the meat so that it cooks more evenly and prevents meat drying out and shrinking during cooking, or the meat near the bone will cook more slowly than the rest of the steak, and the tenderloin will tend to reach the desired temperature before the strip.

Bistecca alla fiorentina
Bistecca alla fiorentina (lit. 'beefsteak Florentine style'), consists of a T-bone traditionally sourced from either the Chianina or Maremmana breeds of cattle. A favorite of Tuscan cuisine, the steak is grilled over a wood or charcoal fire, seasoned with salt, sometimes with black pepper, and olive oil, applied immediately after the meat is retired from the heat. Thickly cut and very large, "Bistecca" are often shared between two or more people, and traditionally served very rare, sometimes garnished with lemon wedges, if not accompanied by red wine, and accompanied by Tuscan beans as a side dish.

Cotoletta alla milanese
The same cut of meat, but from a calf, is used for cotoletta alla milanese, which consists of 1.5 cm-thick cuts which are battered in breadcrumbs and fried in clarified butter with salt.

title: T-bone steak


text:
Divergence of the sum of the reciprocals of the primes

The sum of the reciprocals of all prime numbers diverges; that is: $$\sum_{p\text{ prime}}\frac1p = \frac12 + \frac13 + \frac15 + \frac17 + \frac1{11} + \frac1{13} + \frac1{17} + \cdots = \infty$$

This was proved by Leonhard Euler in 1737, and strengthens Euclid's 3rd-century-BC result that there are infinitely many prime numbers and Nicole Oresme's 14th-century proof of the divergence of the sum of the reciprocals of the integers (harmonic series).

There are a variety of proofs of Euler's result, including a lower bound for the partial sums stating that $$\sum_{\scriptstyle p\text{ prime}\atop \scriptstyle p\le n}\frac1p \ge \log \log (n+1) - \log\frac{\pi^2}6$$ for all natural numbers $n$. The double natural logarithm ($log log$) indicates that the divergence might be very slow, which is indeed the case. See Meissel–Mertens constant.

The harmonic series
First, we describe how Euler originally discovered the result. He was considering the harmonic series $$ \sum_{n=1}^\infty \frac{1}{n} = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \cdots = \infty $$

He had already used the following "product formula" to show the existence of infinitely many primes.

$$ \sum_{n=1}^\infty \frac{1}{n} = \prod_{p} \left( 1+\frac{1}{p}+\frac{1}{p^2}+\cdots \right) = \prod_{p} \frac{1}{1-p^{-1}} $$

Here the product is taken over the set of all primes.

Such infinite products are today called Euler products. The product above is a reflection of the fundamental theorem of arithmetic. Euler noted that if there were only a finite number of primes, then the product on the right would clearly converge, contradicting the divergence of the harmonic series.

Euler's proof
Euler considered the above product formula and proceeded to make a sequence of audacious leaps of logic. First, he took the natural logarithm of each side, then he used the Taylor series expansion for $log x$ as well as the sum of a converging series:

$$\begin{align} \log \left( \sum_{n=1}^\infty \frac{1}{n}\right) & {} = \log\left( \prod_p \frac{1}{1-p^{-1}}\right) = -\sum_p \log \left( 1-\frac{1}{p}\right) \\[5pt] & = \sum_p \left( \frac{1}{p} + \frac{1}{2p^2} + \frac{1}{3p^3} + \cdots \right) \\[5pt] & = \sum_{p}\frac{1}{p} + \frac{1}{2}\sum_p \frac{1}{p^2} + \frac{1}{3}\sum_p \frac{1}{p^3}  + \frac{1}{4}\sum_p \frac{1}{p^4}+ \cdots  \\[5pt] & =  A  + \frac{1}{2} B+ \frac{1}{3} C+ \frac{1}{4} D  + \cdots  \\[5pt] & = A + K \end{align}$$

for a fixed constant $K < 1$. Then he invoked the relation

$$\sum_{n=1}^\infty\frac{1}{n} = \log\infty,$$

which he explained, for instance in a later 1748 work, by setting $x = 1$ in the Taylor series expansion

$$\log\left(\frac1{1-x}\right)=\sum_{n=1}^\infty\frac{x^{n}}n.$$

This allowed him to conclude that $$A = \frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{7} + \frac{1}{11} + \cdots = \log \log \infty.$$

It is almost certain that Euler meant that the sum of the reciprocals of the primes less than $n$ is asymptotic to $log log n$ as $n$ approaches infinity. It turns out this is indeed the case, and a more precise version of this fact was rigorously proved by Franz Mertens in 1874. Thus Euler obtained a correct result by questionable means.

Erdős's proof by upper and lower estimates
The following proof by contradiction comes from Paul Erdős.

Let $p_{i}$ denote the $i$th prime number. Assume that the sum of the reciprocals of the primes converges.

Then there exists a smallest positive integer $k$ such that

$$\sum_{i=k+1}^\infty \frac 1 {p_i} < \frac12 \qquad(1)$$

For a positive integer $x$, let $M_{x}$ denote the set of those $n$ in ${1, 2, ..., x}$ which are not divisible by any prime greater than $p_{k}$ (or equivalently all $n ≤ x$ which are a product of powers of primes $p_{i} ≤ p_{k}$). We will now derive an upper and a lower estimate for $|M_{x}|$, the number of elements in $M_{x}$. For large $x$, these bounds will turn out to be contradictory.

 * Upper estimate:
 * Every $n$ in $M_{x}$ can be written as $n = m^{2}r$ with positive integers $m$ and $r$, where $r$ is square-free. Since only the $k$ primes $p_{1}, ..., p_{k}$ can show up (with exponent 1) in the prime factorization of $r$, there are at most $2^{k}$ different possibilities for $r$. Furthermore, there are at most $√x$ possible values for $m$. This gives us the upper estimate $$|M_x| \le 2^k\sqrt{x} \qquad(2)$$

 * Lower estimate:
 * The remaining $x − |M_{x}|$ numbers in the set difference ${1, 2, ..., x} \ M_{x}$ are all divisible by a prime greater than $p_{k}$. Let $N_{i,x}$ denote the set of those $n$ in {1, 2, ..., x$)$}} which are divisible by the $i$th prime $p_{i}$. Then $$\{1,2,\ldots,x\}\setminus M_x = \bigcup_{i=k+1}^\infty N_{i,x}$$
 * Since the number of integers in $N_{i,x}$ is at most $x⁄p_{i}$ (actually zero for $p_{i} > x$), we get $$x-|M_x| \le \sum_{i=k+1}^\infty |N_{i,x}|< \sum_{i=k+1}^\infty \frac x {p_i}$$
 * Using (1), this implies $$\frac x 2 < |M_x| \qquad(3)$$

This produces a contradiction: when $x ≥ 2^{2k + 2}$, the estimates (2) and (3) cannot both hold, because $x⁄2 ≥ 2^{k}√x$.

Proof that the series exhibits log-log growth
Here is another proof that actually gives a lower estimate for the partial sums; in particular, it shows that these sums grow at least as fast as $log log n$. The proof is due to Ivan Niven, adapted from the product expansion idea of Euler. In the following, a sum or product taken over $p$ always represents a sum or product taken over a specified set of primes.

The proof rests upon the following four inequalities:

To see this, note that $$\frac 1 i = \frac 1 {p_1 p_2 \cdots p_s} \cdot \frac 1 {b^2},$$ and $$\begin{align} \left(1 + \frac{1}{p_1}\right)\left(1 + \frac{1}{p_2}\right) \ldots \left(1 + \frac{1}{p_s}\right) &= \left(\frac{1}{p_1}\right)\left(\frac{1}{p_2}\right)\cdots\left(\frac{1}{p_s}\right) + \ldots\\ &= \frac 1 {p_1 p_2 \cdots p_s} + \ldots. \end{align}$$ That is, $$1/(p_1p_2 \cdots p_s)$$ is one of the summands in the expanded product $p$. And since $$1 / b^2$$ is one of the summands of $i$, every summand $$1/i$$ is represented in one of the terms of $q$ when multiplied out. The inequality follows. \log(n+1) &= \int_1^{n+1} \frac{dx}x \\ &= \sum_{i=1}^n\underbrace{\int_i^{i+1}\frac{dx}x}_{{} \,<\, \frac1i} \\ &< \sum_{i=1}^n \frac 1 i \end{align}$$ \sum_{k=1}^n \frac 1 {k^2} &< 1 + \sum_{k=2}^n \underbrace{\left(\frac1{k - \frac{1}{2}} - \frac1{k + \frac{1}{2}}\right)}_{=\, \frac{1}{k^2 - \frac14} \,>\, \frac{1}{k^2}} \\ &= 1 + \frac23 - \frac1{n + \frac{1}{2}} < \frac53 \end{align}$$
 * Every positive integer $q$ can be uniquely expressed as the product of a square-free integer and a square as a consequence of the fundamental theorem of arithmetic. Start with $$i = q_1^{2{\alpha}_1+{\beta}_1} \cdot q_2^{2{\alpha}_2+{\beta}_2} \cdots q_r^{2{\alpha}_r+{\beta}_r},$$ where the βs are 0 (the corresponding power of prime $i$ is even) or 1 (the corresponding power of prime $A$ is odd). Factor out one copy of all the primes whose β is 1, leaving a product of primes to even powers, itself a square. Relabeling: $$i = (p_1 p_2 \cdots p_s) \cdot b^2,$$ where the first factor, a product of primes to the first power, is square free. Inverting all the $B$s gives the inequality $$ \sum_{i=1}^n \frac 1 i \le \left(\prod_{p \le n} \left(1 + \frac 1 p \right)\right) \cdot \left(\sum_{k=1}^n \frac 1 {k^2}\right) = A \cdot B.$$
 * The upper estimate for the natural logarithm $$\begin{align}
 * The lower estimate $1 + x < exp(x)$ for the exponential function, which holds for all $x > 0$.
 * Let $n ≥ 2$.  The upper bound (using a telescoping sum) for the partial sums (convergence is all we really need) $$\begin{align}

Combining all these inequalities, we see that $$\begin{align} \log(n+1) & < \sum_{i=1}^n\frac{1}{i} \\ & \le \prod_{p \le n} \left(1 + \frac{1}{p}\right) \sum_{k=1}^n \frac{1}{k^2} \\ & < \frac53\prod_{p \le n} \exp\left(\frac{1}{p}\right) \\ & = \frac53\exp\left(\sum_{p \le n} \frac{1}{p} \right) \end{align}$$

Dividing through by $AB$ and taking the natural logarithm of both sides gives $$\log\log(n + 1) - \log\frac53 < \sum_{p \le n} \frac{1}{p}$$

as desired. Q.E.D.

Using

$$\sum_{k=1}^\infty \frac{1}{k^2} = \frac{\pi^2}6$$

(see the Basel problem), the above constant $log 5⁄3 = 0.51082...$ can be improved to $log π^{2}⁄6 = 0.4977...$; in fact it turns out that $$ \lim_{n \to \infty } \left( \sum_{p \leq n} \frac{1}{p} - \log \log n \right) = M$$

where $M = 0.261497...$ is the Meissel–Mertens constant (somewhat analogous to the much more famous Euler–Mascheroni constant).

Proof from Dusart's inequality
From Dusart's inequality, we get $$ p_n < n \log n + n \log \log n \quad\mbox{for } n \ge 6$$

Then $$\begin{align} \sum_{n=1}^\infty \frac1{ p_n} &\ge \sum_{n=6}^\infty \frac{1}{ p_n} \\ &\ge \sum_{n=6}^\infty \frac{1}{ n \log n + n \log \log n} \\ &\ge \sum_{n=6}^\infty \frac{1}{2n \log n} = \infty \end{align}$$ by the integral test for convergence. This shows that the series on the left diverges.

Geometric and harmonic-series proof
The following proof is modified from James A. Clarkson.

Define the k-th tail

$$x_{k} = \sum_{n = k+1} ^{\infty} \frac{1}{p_n}.$$

Then for $$i \geq 0$$, the expansion of $$(x_{k})^{i}$$ contains at least one term for each reciprocal of a positive integer with exactly $$i$$ prime factors (counting multiplicities) only from the set $$ \{ p_{k+1}, p_{k+2}, \cdots \}$$. It follows that the geometric series $\sum_{i = 0} ^{\infty} (x_{k})^{i}$ contains at least one term for each reciprocal of a positive integer not divisible by any $$p_{n},n\leq k$$. But since $$1+j(p_{1}p_{2}\cdots p_{k})$$ always satisfies this criterion,

$$\sum_{i=0}^{\infty}(x_{k})^{i}>\sum_{j=1}^{\infty} \frac{1}{1+j(p_{1}p_{2} \cdots p_{k})}>\frac{1}{1+p_{1}p_{2} \cdots p_{k}} \sum_{j=1}^{\infty}\frac{1}{j}=\infty$$

by the divergence of the harmonic series. This shows that $$x_{k}\geq 1$$ for all $$k$$, and since the tails of a convergent series must themselves converge to zero, this proves divergence.

Partial sums
While the partial sums of the reciprocals of the primes eventually exceed any integer value, they never equal an integer.

One proof is by induction: The first partial sum is $5⁄3$, which has the form $1⁄2$. If the $odd⁄even$th partial sum (for $n ≥ 1$) has the form $n$, then the $(n + 1)$st sum is

$$\frac\text{odd}\text{even} + \frac{1}{p_{n+1}} = \frac{\text{odd} \cdot p_{n+1} + \text{even}}{\text{even} \cdot p_{n+1}} = \frac{\text{odd} + \text{even}}\text{even} = \frac\text{odd}\text{even}$$

as the $(n + 1)$st prime $p_{n + 1}$ is odd; since this sum also has an $odd⁄even$ form, this partial sum cannot be an integer (because 2 divides the denominator but not the numerator), and the induction continues.

Another proof rewrites the expression for the sum of the first $odd⁄even$ reciprocals of primes (or indeed the sum of the reciprocals of any set of primes) in terms of the least common denominator, which is the product of all these primes. Then each of these primes divides all but one of the numerator terms and hence does not divide the numerator itself; but each prime does divide the denominator. Thus the expression is irreducible and is non-integer.


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User talk:Veemon

Hello Veemon, welcome to Wikipedia. I hope you enjoy editing here and being a Wikipedian. You can learn more on the how to edit page. The naming conventions and manual of style pages are also useful. Feel free to experiment at the Sandbox. If you have any questions about the project then check out Help or add a question to the Village pump. Angela

title: User talk:Veemon


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User talk:Robert McGuigan

Hello Robert, welcome to Wikipedia. I hope you enjoy editing here and being a Wikipedian. You can learn more on the how to edit page. The naming conventions and manual of style pages are also useful. Feel free to experiment at the Sandbox. If you have any questions about the project then check out Help or add a question to the Village pump. Angela

Science pearls
Hello,

Since you contributed in the past to the publications’ lists, I thought that you might be interested in this new project. I’ll be glad if you will continue contributing. Thanks,APH 11:02, 11 September 2005 (UTC)

Chryselephantine sculpture
Hi, Thanks for your edits. I always need someone to go over my sloppy typing and occasional messy grammar. I reverted one of your edits, turning "jewelry" back into "jewellery", as the latter is the British spelling, which I prefer, and which wikipedia policy favours in this case, as it was used first. Please don't be offended by that, it's a personal choice, and it does not take away frok my gratitude for your editing efforts. athinaios 23:46, 8 November 2007 (UTC)

Edit summaries and minor flag
Hi Robert. Thanks for your contributions to Wikipedia. I don't know if you knew, but there's a guideline on using Edit summaries. This asks us to fill in the summary field, on each edit we do, and this procedure helps other editors, down the line. Just one other thing, I notice that you use the wp:Minor flag frequently. Please may I ask you to use the flag only when making minor modifications, but not if adding content. Thanks and keep up the good go (game) edits. Trafford09 (talk) 13:06, 27 December 2010 (UTC)

ArbCom elections are now open!
MediaWiki message delivery (talk) 13:05, 23 November 2015 (UTC)

title: User talk:Robert McGuigan