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Talk:Harmonic series (mathematics)

Divergence proofs
can someone explain better why the harmonic series converges? I couldn't follow through in this explanation.

 * Umm, but the harmoic series does not converge. As the article says, it diverges. Gandalf61 09:44, Feb 6, 2005 (UTC)

I learned the harmonic series is equal to the integral:

 * $$H_n = \int_0^1 \frac{1-x^n}{1-x}\,dx $$

as well as a proof based on geometric series (proven by Euler). Do I need to put the proof in the article?

 * I do not see the need for the proof, as the one in there now is quite easy (as proofs go) to understand. I am not aware of the proof you refer to, off the top of my head, so if indeed it is a really neat one, perhaps you could add it.  But my default reaction is no.

 * Are you asking whether to include the integral identity? If so, I would say go ahead.  But note by saying this I am not vouching for its accuracy.

 * Baccyak4H 17:29, 17 August 2006 (UTC)

 * Actually, I would suggest not to include the identity, since the page on harmonic numbers has it. It is better there.  Baccyak4H 14:11, 24 August 2006 (UTC)

Is there a reason that Jakob Bernoulli's 1689 proof isn't cited? It's rather clever and generally regarded as the standard early proof; I hadn't heard of the medieval guy's proof before, though.

General Harmonic series
Can someone restrict what a and b are supposed to be? I'd assume they can be any real number, but it isn't clear. M00npirate (talk) 18:54, 7 February 2009 (UTC)

 * ✅. You are right, so I added "real number" to the article. Should the article mention it's also true for complex numbers? --68.0.124.33 (talk) 15:42, 16 May 2009 (UTC)

∞/∞ = ∞?
1  1   3     3   1   11     11   1   50     50   1   275     275   1   1770          ∞ - + - = -     - + - = --     -- + - = --     -- + - = ---     --- + - =         = - 1   2   2     2   3   6      6    4   24     24   5   120     120   6   720 ...       ∞

Robo37 (talk) 19:20, 16 June 2009 (UTC)
 * Maybe, and maybe not. See limit.  Baccyak4H (Yak!) 19:22, 16 June 2009 (UTC)

More precisely: in some cases, when the numerator and denominator both diverge to infinity, the fraction itself diverges to infinity. In some such cases, the fraction converges to a finite number. In some such cases, the fraction oscillates or otherwise fails to converge without diverging to infinity.

Robo37, why do you write 50/24 instead of 25/12, and 275/120 instead of 55/24, and 1770/720 instead of 59/24? If you write the fractions in lowest terms, it's not so clear that the numerator and denominator diverge to infinity. If the two denominators are 6 and 4, then the least common denominator is 12, not 24. If they are 120 and 6, then it is 120, not 720.

Baccyak4H, when you use the word "maybe", it makes it sound as if you don't know the answer. Michael Hardy (talk) 19:40, 16 June 2009 (UTC)
 * Hmm, it does. Of course, I did know the answer ("maybe" referred to the section heading alone; another such series might not make the header "true").  Baccyak4H (Yak!) 04:28, 17 June 2009 (UTC)
 * I put 50/24 instead of 25/12 275/120 instead of 55/24 and 1770/720 instead of 59/24 simply because multiplying the denominators together was the easiest thing to do. Changing the fractions make little difference, since you are still left with:

3   11    25    55    59    437    ∞ -    --    --    --    --    ---    - 2... 6 ... 12... 24... 24... 168... ∞

 * Thinking about it, the same method can be used to prove that ∞/∞ is any positive number.

9    9     9       9       9         9     9   99     9    999      9 1 = 0.999999999... = -- + --- +  + - + --    = -- + ---  --- +    + -                      10   100   1000   10000   100000...   10   100, 100   1000, 1000   10000, 9999      9     99999       ∞ - + --  --    = - 10000   100000, 100000...   ∞

1  9     9     9       9       9         1   9   19    9   199    9 2 = 1.999999999... = - + -- + --- +  + - + --    = - + --  -- + ---  --- +                       1   10   100   1000   10000   100000...   1   10, 10   100, 100   1000, 1999     9    19999      ∞  + -  -    = - 1000   10000, 10000...   ∞

1                         4     9     9       9       9         4     9   49     9    499 - = 0.5 = 0.499999999... = -- + --- +  + - + --    = -- + ---  --- +    + 2                          10   100   1000   10000   100000...   10   100, 100   1000, 1000   9    4999      9     49999       ∞ -  - + --  --    = - 10000, 10000   100000, 100000...   ∞

1                          2     4     9       9       9         2     4   24     9    249 - = 0.25 = 0.249999999... = -- + --- +  + - + --    = -- + ---  --- +    + 4                           10   100   1000   10000   100000...   10   100, 100   1000, 1000   9    2499      9     24999       ∞ -  - + --  --    = - 10000, 10000   100000, 100000...   ∞

1                3     3     3       3       3         3     3   33     3    333 - = 0.333333333 = -- + --- +  + - + --    = -- + ---  --- +    + 3                 10   100   1000   10000   100000...   10   100, 100   1000, 1000   3    3333      3     33333       ∞ -  - + --  --    = - 10000, 10000   100000, 100000...   ∞

1                1     6     6       6       6         1     6   16     6    166 - = 0.166666666 = -- + --- +  + - + --    = -- + ---  --- +    + 6                 10   100   1000   10000   100000...   10   100, 100   1000, 1000   6    1666      6     16666       ∞ -  - + --  --    = - 10000, 10000   100000, 100000...   ∞

1                1     4     2       8       5         1     4   14     2    142 - = 0.142857142 = -- + --- +  + - + --    = -- + ---  --- +    + 7                 10   100   1000   10000   100000...   10   100, 100   1000, 1000   8    1428      5     14285       ∞ -  - + --  --    = - 10000, 10000   100000, 100000...   ∞

3   1     4     1       5     3   1   31    4   314 π = 3.141592654 = - +  -- + --- +  + - = - + --  -- + ---  --- + 1   10   100   1000   10000   1   10, 10   100, 100   1    3141      5     31415       ∞ -  - + --  --    = - 10000, 10000   100000, 100000...   ∞

Robo37 (talk) 20:03, 17 June 2009 (UTC)

playing it fast and loose in "proofs"
Most of the proofs in this article seem to assume that you can do things like group terms (maybe this works when all terms are positive? Counterexamples are things like 1 − 1 + 1 − 1 + · · ·) and reorder terms (I really don't know what assumption is needed to justify this). In a historical sense, it took some centuries to sort this through, so it probably makes sense to speak of a "proof" which would not be accepted today, or would only be accepted today with elaboration. But we need some kind of disclaimer or clarification (such as "both of these statements can be made precise and formally proven, but only using well-defined mathematical concepts that arose in the 19th century" and surrounding treatment at 1 − 1 + 1 − 1 + · · ·). Kingdon (talk) 01:24, 19 August 2009 (UTC)

 * I don't think the article needs 5 proofs of the divergence in any case; it has the appearance of creep. So I removed the latter two, which were probably the ones you were concerned about anyway. — Carl (CBM · talk) 01:51, 19 August 2009 (UTC)

 * Can we at least have a proof by integral test? (The French version has this.) This proof is not only short but, arguably. more conceptual since it shows the connection to log. -- Taku (talk) 12:10, 19 August 2009 (UTC)

 * I didn't remove the sentence on that, although it is very brief. — Carl (CBM · talk) 21:48, 19 August 2009 (UTC)

 * The approach in such "rearrangement" proofs is to first of all assume that the series is convergent. If this is true then the terms of the series can be grouped or rearranged as we like without affecting the limit. However, if a rearrangement leads to a contradiction, then, by reductio ad absurdum, our original assumption must be incorrect. Therefore the series is not convergent. Not saying the rearrangement proof should be restored - just saying that it is rigorous. Gandalf61 (talk) 16:42, 19 August 2009 (UTC)

 * Proofs like that would be more clear if they pointed out that the series is positive, so absolutely convergent if convergent, and thus allowing rearrangement if convergent. But I don't think that the focus of this article should be a long list of different proofs of nonconvergence of this series; it mentions 2 right now. — Carl (CBM · talk) 21:48, 19 August 2009 (UTC)

 * Hmm, I missed that consequence of the reductio ad absurdum. But I'm fine with deleting the extra proofs, as they did break up the flow of the article. Kingdon (talk) 11:32, 24 August 2009 (UTC)

p-series
If, as the article says, harmonic series are "divergent infinite series" then why include the p-series? Since when p = 2 we have a convergent infinite sequence: we have the famous formula
 * $$ \sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6} \ . $$

In fact, if my memory serves me correctly, all p-series with p ∈ R and p > 1 converge. (Actually ζ(x) → 1 as x → + ∞ )  Dr Dec  (Talk)    13:18, 24 September 2009 (UTC)
 * The inclusion seems appropriate to me since the p-series is a simple generalization that's close enough to the subject. A separate article would be unnecessary since anything additional to say would be in the Riemann zeta function article.--RDBury (talk) 12:57, 25 September 2009 (UTC)
 * But this "inclusion" includes a set of objects which contradict the definition. Taking p ∈ R, then an open and dense set of p-series are not divergent, and so are not harmonic series, and so the inclusion is not valid. Either the definition, that harmonic series are "divergent infinite series", needs to be changed (which is clearly not a good idea) or the example needs to be re-worded. Dr Dec  (Talk)   23:04, 25 October 2009 (UTC)

 * The harmonic series is one specific divergent series - the sum of the reciprocals of the positive integers. I have re-worded the p-series section to make it clear that the p-series are a generalisation of the harmonic series - the harmonic series is the special case of a p-series when p=1. Gandalf61 (talk) 09:46, 26 October 2009 (UTC)

How slowly does it diverge?
I have thought about this statement and calculated that it is way off. If we imagine the sum of the sequence 1 + (1/2) + (1/4 + 1/4) + (1/8 + 1/8 + 1/8 + 1/8)... we can see: each group of terms (in brackets) is equal to 1/2. In every next group, the number of terms is twice as big (because each term is halved). If we have n groups, then to find the number of terms, we have to add 1 + 2 + 4 + 8... + 2n - 1, which is a geometric progression with a common ratio of 2. We will start the addition from the other end, to make it a progression just like 1 + 1/2 + 1/4 + 1/8... = 2. So, for very large n, the number of terms will be about twice the number of groups. So, if we have 1043 terms, then we will have 5 × 1042 groups, each of which equals to 1/2. Thus this sum will equal to about 2.5 × 1042, which is unimaginably far larger than 100! And knowing that the harmonic series grows faster than the series here (which was used to prove the divergence of the harmonic series), this means that the sum of that many terms of the harmonic series will be ever bigger.Majopius (talk) 02:20, 6 February 2010 (UTC)

 * Sorry—you've mangled your math. If you have n groups, you've got the sum > n×(1/2).  But how many terms does it take to make n groups?  If you have 1043 terms, then how many groups do you have, each exceeding 1/2?
 * If you have n groups, then you have 2n − 1 terms. If you have 200 groups (so that the sum exceeds 100), then you have 2200 − 1 terms, or about 1.6 × 1060.
 * Now let's try something less crude:
 * $$ {1\over2} + {1\over3} + {1\over4} + \cdots + {1\over n} < \int_1^n {dx \over x} < 1 + {1\over2} + {1\over3} + {1\over4} + \cdots + {1\over n -1}$$
 * and
 * $$ \int_1^n {dx \over x} = \log_e n = {\log_{10} n \over \log_{10} e}. $$
 * If n = 1043 then this is 43/log10 e = about 99.
 * So: Yes, really. The article's claim is correct. Michael Hardy (talk) 05:02, 6 February 2010 (UTC)
 * and
 * $$ \int_1^n {dx \over x} = \log_e n = {\log_{10} n \over \log_{10} e}. $$
 * If n = 1043 then this is 43/log10 e = about 99.
 * So: Yes, really. The article's claim is correct. Michael Hardy (talk) 05:02, 6 February 2010 (UTC)
 * If n = 1043 then this is 43/log10 e = about 99.
 * So: Yes, really. The article's claim is correct. Michael Hardy (talk) 05:02, 6 February 2010 (UTC)
 * So: Yes, really. The article's claim is correct. Michael Hardy (talk) 05:02, 6 February 2010 (UTC)

 * I did not mangle anything! I was attentive when thinking about it, and got this result. Oh well, its a paradox.Majopius (talk) 18:33, 6 February 2010 (UTC)

 * You said "...the number of terms will be about twice the number of groups". Actually, the number of terms is about two to the power of the number of groups. Gandalf61 (talk) 14:36, 9 February 2011 (UTC)

For primes Sum(1/p)  already diverges: is this worth mentioning?195.96.229.83 (talk) 11:33, 9 February 2011 (UTC)

Comparison Test Formula
A minor suggestion and it might just be based on how my brain works, but I find this...

$$\sum_{n=1}^{2^k} \,\frac{1}{n} \;>\; 1 + k(\frac{1}{2})$$

...easier than this...

$$\sum_{n=1}^{2^k} \,\frac{1}{n} \;>\; 1 + \frac{k}{2}$$

...when making the mental jump from the expanded series above to the summation notation. —Preceding unsigned comment added by 207.164.58.11 (talk) 17:48, 29 June 2010 (UTC)

Shouldn't the inequality be a weak inequality? After all, the two sides are equal at k = 1. — Preceding unsigned comment added by 134.10.12.152 (talk) 22:13, 8 June 2011 (UTC)

Cauchy Criterian test
If we apply the CC test then the convergence is equivalent to asking if 1+1+1+1..... converges, and obviously it doesn't. Its "neat" so I thought maybe someone should add a section this. — Preceding unsigned comment added by 99.149.190.128 (talk) 04:08, 13 September 2012 (UTC)
 * Cauchy's convergence test?? We can even show partial sum is not Cauchy sequence. Will add it. 91.76.22.132 (talk) 19:30, 15 May 2020 (UTC)

Could the general harmonic series start from any number?
The article currently defines the general harmonic series as:

 * $$\sum_{n=0}^{\infty}\frac{1}{an+b}.\!$$

Couldn't the 0 be replaced with an additional variable, such as $$c$$? After all, I'm pretty sure you can always remove a finite number of terms from the start of a divergent series and it has to remain divergent. ± Lenoxus (" *** ") 15:04, 20 March 2013 (UTC)

 * Yes, but

 * $$\sum_{n=c}^{\infty}\frac{1}{an+b} = \sum_{n=0}^{\infty}\frac{1}{a(n+c)+b}=\sum_{n=0}^{\infty}\frac{1}{an+d}.\!$$

 * where d = ac + b. So if you start the summation at c it is still part of the same family. And, as you say, still a divergent series. Gandalf61 (talk) 15:13, 20 March 2013 (UTC)

 * Ah, very nice. We can change the 0 but may as well change the b. Thanks. ± Lenoxus (" *** ") 16:55, 20 March 2013 (UTC)

General harmonic series: I give up!
A period after the equation ended the sentence early, and try as I might, I can't seem to change it to a [space]comma even though there is a space before the comma in the next equation, the one for the P-series.

HELLLP!

Also, is there a way to get math html to render in edit preview mode? I wouldn;t have had to make so many damn wrong edits if I could have previewed before saving. Dave Bowman - Discovery Won (talk) 12:35, 8 April 2013 (UTC)

alternative summation?
This page demonstrates that, viewed in the traditional light, the harmonic series is divergent. However, many other divergent series have what one might term 'creative' summations using alternative techniques. (See 1 − 1 + 1 − 1 + · · ·, 1 + 2 + 4 + 8 + · · ·, 1 + 1 + 1 + 1 + · · ·, 1 + 2 + 3 + 4 + · · ·, and so forth; and Cesàro summation, Ramanujan summation, and so forth.)

So what about the harmonic series? What alternative summation techniques have mathematicians applied to it? Doops | talk 05:14, 15 January 2014 (UTC)

 * Somewhere among these blog articles https://cornellmath.wordpress.com/2007/07/28/sum-divergent-series-i/ (in comments, IIRC) I've seen it being summed to the Euler-Mascheroni constant.--Alexmagnus (talk) 00:21, 31 October 2015 (UTC)

Integral Test
The section says "However, the total area under the curve y = 1 / x from 1 to infinity is given by an improper integral" which is stated to equal infinity. No justification is given for that(ie. proof of divergence). JDiala (talk) 03:53, 16 February 2014 (UTC)

Alternating Harmonic Series, no calc
Assuming $$e^x\ge x+1$$ for all x, and without using calculus (no limits, differentiation, integration, or epsilon-delta — that is, only using stuff a precalc student could theoretically do), it is possible to prove the following:

$$\ln2-\frac1n<1-\frac12+\frac13-\dotsb\frac1n<\ln2+\frac1n$$

Then, the Squeeze Theorem immediately tells us that the alternating harmonic series converges to $$\ln2$$.

(I don't have time to provide a proof, but try substituting things like $$x=\ln\frac{100}{99}$$ and $$x=\ln\frac{99}{100}$$ into the above inequality and see what happens. Remember that $$1-\frac12+\frac13-\dotsb\frac1{n}=\frac1{\lfloor n/2\rfloor+1}+\frac1{\lfloor n/2\rfloor+2}+\dotsb+\frac1{n}$$.) — Preceding unsigned comment added by 66.108.7.224 (talk) 10:31, 24 March 2015 (UTC)

Other proofs of divergence (as a last section)
I thought it would not be bad to have another few proofs of the divergence, maybe not in full details as the two in the current version. The current article is nice, but (IMHO) it is still too close to the standard tradition of calculus textbooks. I added two more proofs, that were deleted -- for various objections mentioned on the history page; these may have some good reasons, but none of them seems really strong). In particular, this material is definitely not "original reserch" (recall the "Paris is the capital of France" example). Instead it is some old arguments maybe not universally known: but the point we should discuss is not if they are well-known enough to enter an encyclopedia, but if they are worth.

My proposal is to leave were it is the "comparison proof", and move in a last section named "other proofs" the "integral test" together with the other two I provided. I copy them here below. The scope of this last section should not be to add strength to the proof (one proof is enough), but instead to show connections with other tools and ideas in mathematics.

Comparison II
Whether the harmonic series is finite or not,  we can write it as a sum of two series:
 * $$\begin{align}

\bigg(1 &+ \frac{1}{3} + \frac{1}{5} + \frac{1}{7} + \frac{1}{9}  + \cdots\bigg) +\\ \bigg(\frac{1}{2} &+ \frac{1}{4} + \frac{1}{6} + \frac{1}{8} + \frac{1}{10} +  \cdots\bigg) =\\ 1 &+ \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \dots \end{align}$$ The terms of the second series are strictly less than the corresponding terms of the first one, so the sum of the second series is strictly less than the sum of the first one, provided the sum is finite. But in fact these two sums are equal: indeed, the second series, thus the first one too, is exactly one half of the harmonic series. Since the sum can't be finite we conclude it is infinite. Note: one main objection was "It relies on results about rearranging series that are much more sophisticated than what is being proven": this is quite wrong (there is no rearrangement, which by the way for positive series is almost as elementary as the notion itself of sum of a positive series, but less more that term-wise sum of series)

In a simpler version:

Comparison II -bis
Majorize each odd term oh the harmonic series with the following even term:
 * $$\begin{align}

1 &+ \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5}  + \frac{1}{6}  \cdots  \ge \\ \frac{1}{2} &+ \frac{1}{2} + \frac{1}{4} + \frac{1}{4} + \frac{1}{6} +  \frac{1}{6}   \cdots  =\\ \bigg(\frac{1}{2} &+ \frac{1}{2}\bigg) + \bigg(\frac{1}{4} + \frac{1}{4}\bigg) + \bigg(\frac{1}{6} +  \frac{1}{6}\bigg)   \cdots  =\\ 1 &+ \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6}\dots \end{align}$$ However, if the harmonic sum where finite, the above inequality would be strict, which is impossible, therefore the sum is infinite.

Note: grouping the pairs of consecutive equal terms in the second sum just corresponds to taking a subsequence of the sequence of partial sums, which should remove any fear about rearrangements that may confuse the freshman

Via dominated convergence (by contradiction)
A proof by contradiction, that uses the dominated convergence theorem in the sequence space ℓ1 goes as follows. Consider the following sequence of unit-norm elements un of ℓ1:
 * $$u_1:=\big(1,0,0,\dots\big)$$
 * $$u_2:=\Big(\frac{1}{2},\frac{1}{2},0,0,\dots\Big)$$
 * $$u_3:=\Big(\frac{1}{3},\frac{1}{3},\frac{1}{3},0,0,\dots\Big),$$

and so on. Clearly the sequence un converges point-wise to 0; moreover it is dominated by
 * $$h:=\Big(1,\frac{1}{2},\frac{1}{3},\frac{1}{4},\dots\Big)$$

If the harmonic series were convergent, that is, if h were an element of ℓ1, by dominated convergence we would conclude
 * $$1=\sum_{k=1}^\infty u_{n,k} \to0$$ as $$n\to+\infty$$, a contradiction.

''Note: I would prefer not to quote the sequence space ℓ1 at all, but just a dominated convergence theorem for series", again a quite elementary fact.

Let me know your opinions. pm a 17:31, 25 July 2019 (UTC)

Discussion
In MOS:MATH, one can read This means that it is not useful to provide all existing proofs. The first proof that is given here is probably the simplest possible (the is the one that requires the minimal mathematical background), and deserve thus to be there. The second one is also useful, as appearing in many textbooks, and is a good introduction on the strong relation between harmonic series and logarithm.

For adding other proofs, it does not suffice that they exist. One must explain how they "illuminate" the subject of the article. Such an explanation has not been given so far. Moreover both involve concepts that a reader is not supposed to know at this part of the article. The new proposed proof (Comparison 2) is also more complicated of the first previous first proof, as needing to understand that $x + y = x$ and $y > 0$ imply that $x$ is infinite.

For these reasons, I oppose to the addition of any of these new proofs. D.Lazard (talk) 11:54, 26 July 2019 (UTC)

 * Thank you D.Lazard. Let me distinguish, because I partially agree. I personally warmly agree that wikipedia should not include a bunch of detailed proofs. Rather, what is important, in the very etymological sense, is to give the information that a certain proof was made (if it is worth), where or how to find the details, and the connections with other ideas. In particular, these articles should not mimic a calculus textbook (btw: IMHO the style of the current version goes a bit too much in that direction, but sure I don't want to add to the controversy). The idea I had in mind is to quote and briefly describe the relevant existing proofs in a last section, not in full details, possibly with the coordinates and links to fill them up, and possibly with a source (unfortunately, at the moment we have it only for the first one; I guess a successful search would bring us to to Euler or Bernoulli). To make an example: several proofs are listed for the Pythagorean theorem, for the fundamental theorem of algebra, for the Euclid's theorem on the infinitude of primes &c. (You'll say: but these theorems are quite more important. I'll answer: true, yet the harmonic series also has its place in the development of analysis, and deserves its list of proofs).pm a 20:59, 26 July 2019 (UTC)
 * In particular, I would give much more emphasis to the historical proofs already mentioned, at the moment almost hidden in notes pm a 22:58, 26 July 2019 (UTC)

 * I agree with D.Lazard. In addition to the objections he raises, all evidence suggests you came up with these proofs yourself, which is a clear-cut violation of WP:OR. --JBL (talk) 20:59, 27 July 2019 (UTC)
 * Do not trust too much what all evidence suggests to you, for she often just likes to make fun of simpletons ;) pm a 22:02, 12 October 2020 (UTC)

 * I'm also obliged to respond to the request One must explain how they "illuminate" the subject of the article. I need then to enlarge the discussion. let's talk of Applications: — Preceding unsigned comment added by PMajer (talk • contribs)
 * "first proof that is given here is probably the simplest possible" This is insanity. It is incorrect per se, we cannot put the brackets as we want (see comments "playing it fast and loose in "proofs"" above). It is also from Mid Ages. "The second one is also useful" Really? Normal math texts cannot use this proof, OMG. Using integrals to prove elementary series problem? Wow. No, everybody uses direct proof that this is not Cauchy sequence or the telescopic proof. I will add the second then. 91.76.22.132 (talk) 21:08, 15 May 2020 (UTC)

 * The first given proof, which, as far as we know, is also the first one in history, is indeed the simplest, and it is perfectly correct. pm a 22:02, 12 October 2020 (UTC)
 * No, it is formally incorrect. Read Cesaro summation and Riemann series theorem. I will quote Riemann for you: "if an infinite series of real numbers is conditionally convergent, then its terms can be arranged in a permutation so that the new series converges to an arbitrary real number, or diverges [or partial sums limit will not exist at all]". And it is not obvious that for positive series we do not care about this. THAT also requires a proof. 109.252.90.66 (talk) 08:22, 16 February 2021 (UTC)
 * That no series of positive terms is conditionally convergent is obvious from the definition, and this kind of bracketing is not a "rearrangement" in the sense of RST (precisely: for any convergent series (conditionally or otherwise), if you bracket terms into consecutive blocks to form a new series, then the new series also converges, to the same limit). Everything in this proof is completely correct. --JBL (talk) 11:54, 16 February 2021 (UTC)

Applications
Indeed this section has a big question mark on it. The applications given are certainly nice stories, a couple of them I think taken from Martin Gardner; we may call them metaphores, or exampla ficta, made to illustrate the facts. The worm on the rubber band is a nice little story, suitable to visualize the mathematical phenomenon, and gives to it some funny consistency and Lewis Carrol's flavor. So far, so good. But calling these stories applications is terribly misleading and diseducative. Even the length of this sections, the abundance of details, and the emphatic position it has at the beginning, are misleading. The important facts, that such an article must recall and stress, are simple, basic and powerful ideas, their genesis and their history. An easy argument like $$x+1=x$$ implies $$x=\pm\infty$$, in its simplicity (formally it's no more than $$x+1>x$$ for any real $$x$$) is fundamental in the whole treatment of the analysis of infinite. It is indeed the key point both in Bernoulli's and in Mengoli's proofs (mentioned, but hidden, in the article), and in its variation I reported. Instead of asking if a series like this converges or diverges, we give in any case a sense to its sum $$S$$, and then we use an extended set of algebraic and order rules to deduce $$S=+\infty$$. It is the same powerful line of reasoning that pervades the development of all mathematics. I guess that the reader that find complicated $$(x+y=x, y>0)$$ implies $$x=\pm\infty$$ will also very easily believe that mathematics is about studying crazy situations involving somebody swimming in a pool for a time larger than the age of the universe, at a speed larger than light's.  This is very bad. No surprise they close maths departments.

Here is a tentative proposal for this section: the title of this section may be changed into Exemples or Harmonic series stories or Harmonic series in pop culture, but Applications really doesn't go. I'll try and change it into Examples; maybe you have a better idea. (I also think it should also better to shorten it and put in the bottom of the article, for the reason I explained, and expand the initial part were the various proofs are mentioned, but this has to be discussed carefully). pm a 19:01, 27 July 2019 (UTC)

 * I strongly dislike the section title "Examples"; "Applications" was far more accurate. Moving it lower in the article would be fine.  --JBL (talk) 21:02, 27 July 2019 (UTC)
 * I agree with : The object of the section is "Examples of use", and this is exactly what is an application. D.Lazard (talk) 08:56, 28 July 2019 (UTC)
 * Dear users, as I wrote, "Examples" was a tentative. I'm confident you'll find something better: please make an effort. "Applications" is inaccurate and misleading as I tried to explain to you. An "application of X" is something more than just an "example of use of X": it is an example of use of X, that motivates the introduction/creation of X. However, may I say, it seems to me that you are taking this thing a bit too much on the personal side, and this is an obstruction to accept improvements. So I will not make further edits, till this discussion reaches some conclusion. pm a 21:14, 30 July 2019 (UTC)
 * An "application of X" is something more than just an "example of use of X": it is an example of use of X, that motivates the introduction/creation of X. This may be your belief, but it strikes me as idiosyncratic. I also see no indication that anyone is taking anything personally. --JBL (talk) 21:55, 30 July 2019 (UTC)

 * I do believe something struck you. I said this article lacks serious and motivating applications, and instead sells silly stories, as applications. Which is misleading. You may call it idiosyncratic: but giving motivating applications is how good divulgation (and teaching) works. Let me repeat the question: How is that you guys are afraid that a reader may find it too difficult to understand "$$x+1=x$$ implies $$x=\pm\infty $$", but you are not afraid that the same person may believe that the study of divergent series is well motivated by the application to silly stories? Or maybe you guys are really convinced that divergent series are aimed to this. The model of a  hypothetical guy swimming on and off till the end of the universe, and possibly even after.
 * PS: What about (no irony): "Application to riddles"? At least it's accurate. pm a 23:12, 30 July 2019 (UTC)

 * Well, I now agree with you that someone seems to be taking this personally. Unfortunately I don't have anything constructive to say in response to your comments, since they do not seem to be responsive to anything anyone else has written. (I am a bit surprised you haven't taken advantage of the evident consensus to move the Applications section lower in the article, as you proposed; perhaps I shall do it myself.) --JBL (talk) 01:44, 31 July 2019 (UTC)
 * No need to be surprised - I'd like to have a constructive discussion, in order to improve the thing, and I believe my suggestions may help. There will be time for moving/changing/adding material when (if) we reach a consensus. pm a 19:16, 31 July 2019 (UTC)

"Discussion". Attic Salt (talk) 23:25, 30 July 2019 (UTC)
 * Is this a proposed alternate title for the section? Or something else? --JBL (talk) 01:48, 31 July 2019 (UTC)
 * Yes. Alternative title for miscellaneous section. Attic Salt (talk) 02:00, 31 July 2019 (UTC)

Proof using the sequence of partial sums
Lets take $$ H_n=\sum_{k=1}^n \frac{1}{k}=1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \cdots +\frac{1}{n}.$$ Now we will show that this sequence is not Cauchy sequence, i.e., that $$\exists \varepsilon>0: \forall k\in \mathbb{N}\ \exists n>k,\exists p \in \mathbb{N}: \left \vert H_{n+p}-H_n \right \vert\geq \varepsilon.$$ Lets subtract $$\left \vert H_{n+p}-H_n \right \vert=\frac{1}{n+1}+\cdots+\frac{1}{n+p}\geq\frac{1}{n+p}+\cdots+\frac{1}{n+p}=\frac{p}{n+p}.$$ Let $$p\doteq n.$$ Then $$\forall n \in \mathbb{N}: \left \vert H_{2n}-H_n \right \vert\geq \frac{1}{2}.$$ Thus, this sequence is not Cauchy sequence and is divergent. By definition the series also diverges.

This is a very important result as it uses very simple math (the first or second theme in calculus) and the definition of series convergence. The integral test is dubious and requires rather good knowledge of practical applications and anyway they come after series usually or with them; Oresme test is not correct anyway unless you will define summation rules properly in your method (inserting zeros and rearranging). This comes much later. 2A00:1370:812C:DB93:4C5A:7358:27B4:89F (talk) 20:25, 15 May 2020 (UTC)

 * A few points. What you've added is written very poorly: bad English and bad math style (full of dense symbols that aren't necessary here).  In terms of what a reader is likely to have seen, basic series tests like direct comparison and the integral test are usually introduced earlier and to a much wider audience than the Cauchy criterion for convergence of sequences.  In spirit, this doesn't really offer any insight into what's going on beyond the direct comparison proof – finding runs which add up to at least 1/2 arbitrarily far into the series.  So it doesn't really add anything new by including it.  Coupled with the fact that the source isn't in English (which isn't automatically disallowed, but is discouraged when English sources are readily available), there are too many reasons not to include this. –Deacon Vorbis (carbon • videos) 21:39, 15 May 2020 (UTC)
 * I added another proof that is used everywhere, telescoping proof. Cauchy criterion is introduced the same time here. LOL. It is very simple. You must show at least two proofs of Harmonic Sequencies on exams usually... Just saying. I will not find English source for you, I did WP:ONUS technically. Why are you reverting? 2A00:1370:812C:DB93:80CE:FB82:3BB2:B836 (talk) 21:59, 15 May 2020 (UTC)
 * Also, "full of dense symbols" is just formal definition of non-Cauchy sequence, one can skip it. 2A00:1370:812C:DB93:80CE:FB82:3BB2:B836 (talk) 22:05, 15 May 2020 (UTC)
 * I agree with Deacon Vorbis. --JBL (talk) 22:23, 15 May 2020 (UTC)
 * look into second proof then. Again this is just wrong, both "proofs" are garbage. 2A00:1FA0:46E1:941E:147F:5EC2:B1C:7931 (talk) 22:29, 15 May 2020 (UTC)
 * Please stop. There are zillions of possible proofs of the divergence of the harmonic series.  Your second proof is cute; that does not mean it needs to be in the article, particularly uncited.  The Cauchy criterion proof is a pointlessly technical belaboring of the beautiful idea of the Oresme proof and does not add anything to an encyclopedic understanding of the harmonic series. --JBL (talk) 22:41, 15 May 2020 (UTC)
 * "Cute" Really? The proof that is used in all textbooks here (at least in 6 of them) is just cute to you? Wow. Okay, if you want to have pathetic article for school so be it. 2A00:1370:812C:DB93:80CE:FB82:3BB2:B836 (talk) 23:15, 15 May 2020 (UTC)

Ad-hoc reasoning in divergence proof
The current version of section "Comparison test" uses sloppy reasoning which gives the reader a wrong impression about calculating with infinite series.

In the first indent (the inequation), the Direct comparison test is used - it is mentioned later (i.e., in the wrong place).

The second indent regroups an infinite series without even mentioning the rearrangement theorem (absolute convergence). A naive reader will get the impression that there is no problem with rearranging any series.

While all this could be fixed, it is unnecessary. I made a suggestion for a shorter argument here, but was reverted by. I'd be willing to fix my messing up of the formula alignment, if this was the only reason of reversion. One aspect would of course be the original version of Oresme; however, I couldn't yet find it. - Jochen Burghardt (talk) 15:49, 2 October 2020 (UTC)

 * Meh. A short note about grouping terms would be okay and should be enough here. The terms in the series are all positive, so there are no issues anyway.  And besides, the grouping isn't even strictly necessary; it's mainly just there for clarity to the reader that we're getting runs of terms that all sum to 1/2. –Deacon Vorbis (carbon • videos) 16:13, 2 October 2020 (UTC)

 * I agree with DV about the lack of a problem with the longer form. The shorter version packages exactly the same idea in a more technical (so harder-to-grasp) formulation, without any real advantage.  (I have no idea what Oresme actually wrote, but I'd bet actual money it looked more like the long version than the short one.) --JBL (talk) 00:13, 3 October 2020 (UTC)

 * You'd lose it. Here's Oresme's proof:

 * I argue that the whole will become infinite. This is proved by this way: there exist an infinite number of parts each of which being greater than one half, and therefore the whole will become infinite. The first is evident, because the fourth part and the third part are more than one half, the same with the fifth up to the eigth part and with the ninth to the sixteenth part, &c, in infinitum.
 * pm a 21:45, 12 October 2020 (UTC)

 * ??? That ... looks much more like the long version than the short version, as I said. --JBL (talk) 22:10, 12 October 2020 (UTC)
 * Maybe because the short and the long are also quite similar to each other. But the above short version by turns out to be the exact translation into formulas of Oresme's words. The present long version have some more details, that seems to me avoidable. In fact the short version seems superior to me. Anyway, the original Oresme's proof may be worth a footnote, like other quotations from Mengoli and the Bernoulli. I found in Sourcebook in the Mathematics of Medieval Europe and North Africa; unfortunately, I wasn't able to find the original Latin text.pm a  22:53, 12 October 2020 (UTC)
 * Your comments appear to miss entirely the point of the differences between the proofs. The Oresme proof you've quoted, like the longer version, avoids being over-burdened by the pedantic and unnecessary technical details. --JBL (talk) 23:21, 12 October 2020 (UTC)
 * Dear JLB, to me both versions are OK, (with a light preference to the shorter, as I said, and maybe the original is even better). We all want to avoid pedantic and unnecessary technical details, but I am honestly curious about your reasoning. Would you clarify your last sentence? How is that the shorter version is more burden by details than the longer? What details do you see in the shorter that are not in the longer? Thanks pm a 08:41, 13 October 2020 (UTC)
 * The long version was understandable a few centuries before Newton, and should be understandable today by any moderately bright 12 year-old. The short version takes this simple idea and wraps it in a modern jargon (an arbitrary positive integer k, switching between infinite sums and finite sums, most especially "sufficiently large") that will be unfamiliar to and not decipherable by anyone who has not taken a first class in proof-based calculus.  This modern machinery is great and is useful for many things, but it is not necessary here and it interferes with clearly communicating the central idea of the proof. --JBL (talk) 13:04, 13 October 2020 (UTC)
 * I see, you refer to "Therefore, the partial sums grow beyond every number, if k is chosen sufficiently large". This is also alluded in the inequality reported in the long version, which is the key point of the proof. Note however that what you call "modern machinery" are ideas that were perfectly clear to the Hellenistic mathematics, to whom we owe them: avoid talking about "infinite processes", like "a sum of infinite objects", which is not an idea that simple and clear, and introducing instead some quantifiers. Anyway, I like the present version as well. pm a 13:40, 13 October 2020 (UTC)

History
To be precise, the second sentence:

 * Proofs were given in the 17th century by Pietro Mengoli, Johann Bernoulli, and Jacob Bernoulli

is slightly inaccurate, according to the given links: Mengoli's proof dates 17th century, but Johann Bernoulli's came in the middle of the 18th century, [no, his 1742 book was just published posthumous] and Jacob Bernoulli did not authored another proof, but just published his brother's. It could also be observed that the Bernoulli brothers were not aware of the preceding proofs, given that Jacob writes "My brother first discovered this.." pm a 21:14, 12 October 2020 (UTC)
 * Bernoulli's argument is also nice; since it is not easy to find it in the linked Latin text, I'll report it in the footnote, like Mengoli's, and see as it looks like.pm a 11:43, 13 October 2020 (UTC)

Comments
Reference 2, Kullman (2001), is cited to support the claim that Johann Bernoulli proved the series' divergence, but it only mentions Jacob Bernoulli (under the name Jacques Bernoulli).

Reference 14, Havil (2003), appears not to actually use the term harmonic number — it just uses $$H_n$$, in all the instances I can find. "No property is more unexpected than $$H_n$$'s divergence, and it is this that Oresme proved", etc. I'm actually a bit puzzled by this, since the terminology is so well established.

In the "Crossing a desert" example, leuca is undefined, though in context it's clearly a measure of distance. The source says that one leuca is 1500 double paces, or about 1.5 miles. Perhaps this should be worked into the text. XOR'easter (talk) 01:07, 9 March 2022 (UTC)

 * Euler's conclusion that the partial sums of reciprocals of primes grow as a double logarithm of the number of terms has been confirmed by later mathematicians as one of Mertens' theorems, and can be seen as a precursor to the prime number theorem. The statement looks right, but the source provided does not include a specific mention of Mertens' theorems. Maybe it should be supplemented? XOR'easter (talk) 18:35, 12 March 2022 (UTC)

p-series links here but is gone.
The link here: P series links to this page, but this page doesn't mention p-series anymore. DeathOfBalance (talk) 23:24, 31 July 2022 (UTC)

 * Convergence_tests also points here. 66.44.49.56 (talk) 02:18, 1 August 2022 (UTC)
 * So it happened in this edit by, part of the process that led to this article reaching good article status, which reframed it as a section about the Riemann zeta function. As far as I can tell, the only remaining discussion of the "p-series test" (a standard, if not terribly important, part of single-variable calculus courses) in Wikipedia is in the article Convergence tests.  It seems to me like that is the natural home for content related to the convergence test.  I'll re-target the link at P series. JBL (talk) 18:54, 1 August 2022 (UTC)

Approximation
Hi,

Sorry if this is not how to do it - it's my first time to suggest something on Wikipedia, and I don't want to mess up an article, especially one with a "good article" designation, by "just editing"! But here's a concern: the article, at the very beginning, says:

"The first n terms of the series sum to approximately ln n + gamma, where ln is the natural logarithm and gamma is the Euler–Mascheroni constant."

However, I think this is wrong (easy to see with Excel). Instead, ln(n) + 1/(2n) + gamma, see: https://mathschallenge.net/full/harmonic_sum_approximation

Also, I think it's confusing to use "n" here because "n" is the variable in the 1/n sum term above, I think it would be better to use, e.g., "k" in this statement. 129.240.66.34 (talk) 10:21, 17 March 2024 (UTC)

 * The lead says . This is correct, since the difference between the sum of the $n$ first terms and $$\ln n + \gamma$$ is less than $$1/n$$ and tends to zero when $$n$$ tends to infinity. However, the term $1/(2n)$ is important in some contexts, since it reduces the approximation error from less than $1/(2n)$ to less than $1/(8n2)$, which is much smaller. See . D.Lazard (talk) 11:05, 17 March 2024 (UTC)

title: Talk:Harmonic series (mathematics)


text:
User:Andrewa/wisecracks

''A few wisecracks that might help lighten VfD and similar battles, by linking to them rather than making the debate overly verbose. I intend this to grow. Unless attribution is shown or disclaimed they are original.''

''Please don't add your own, make your own user page instead! You'll need a userid of course, and this will cost you nothing. Send me a message on my talk page if you like, and I might use your wisecracks too if I like them, or even link to them from here. It's all released under the GPL, of course.''

''The format a bit is patchy you will notice. Please don't fix it, or at least not here. It's the way I think it's most effective. If you think otherwise, again please simply create your own user page. Attributions on the original bits if you use them are hereby requested. Andrewa''

Human
If you make a mistake, don't worry, you're human

If you make the same mistake twice, not a problem, you're normal

If you make the same mistake 1,000 or more times per second, pack it, you're a computer.

cannibal
Flanders: A sequence of yums ran 'round the table: Yum Swann: Yum Flanders: Yum Swann: Yum Flanders: Yum Swann: Yum Flanders: Yum...

- from The reluctant cannibal by Flanders and Swann.

ants
One day I watched ten ants moving a dead earthworm towards their nest. They were behaving in very busy, hardworking antsy fashion.

Two were pulling it towards the nest, one was behind pulling in the opposite direction, and there were three on either side all seemingly pulling sideways in their respective directions. The tenth was on top and seemed to be pulling straight up. But between them, the net force was one antpower pulling towards the nest, and they were making steady progress.

Wikipedia is a bit like that.

And the fascinating thing about those ants was, had I removed any one of eight of those ten, progress towards the nest would have stopped as a result. Food for thought?

Democracy
Democracy is based on the principle that a million men are more likely to be right than one man...

Autocracy is based on the principle that one man is more likely to be right than a million men. Let's have that one again too...

- Lazarus Long, in Time Enough for Love, a novel by Robert A. Heinlein.

prejudice
The difference between a prejudice and a conviction is that you can explain a conviction without getting mad. - Marginal comment in Reader's Digest, date, page and exact wording long forgotten.

(On 10May12 I read the above (exactly as written) in Quotable Quotes in the Nov 77 Reader's Digest attributed to B.M.)

hang in there
don't let the bastards grind you down

Original author unknown, boilerplate nill illegitimus carborundum

the Theodore Chipmunk theorem
Alvin: We've almost got you, Theodore.

Theodore: Almost doesn't count. That big hole almost got me too!

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

title: User:Andrewa/wisecracks


text:
Talk:National Peasants' Party

Untitled
This article links to Christian-Democratic National Peasants' Party, but that's currently just a link back to this article. -- Jmabel | Talk 23:21, Feb 4, 2005 (UTC)

Hundreds of thousands of its members were imprisoned ?!? This was technically impossible. Anonimu 11:19, 16 September 2006 (UTC)

Proposed merge
 Strongly oppose merge to National Peasant Christian-Democratic Party (Romania). While that recent (now renamed) party claimed this party as an ancestor, they are quite distinct parties from different eras, with no continuity to speak of through the Communist era. - Jmabel | Talk 22:38, 23 September 2006 (UTC)
 * Didn't Raţiu and Coposu provide some sort of continuity? If by 'continuity' you mean inside Romania, clearly there was none, but those two men were not unimportant in the inter-war party and key figures when it was restarted in the early 1990s. Biruitorul 01:44, 24 September 2006 (UTC)
 * Yeah, there is some continuity (as I suppose there was for the National Liberals), but it really seems to me to be more useful to handle them in two separate articles. Among other things, it lets us disambiguate more clearly from other articles.
 * In general the handling of Romanian political parties has grown like Topsy. I'd be a lot more amenable to coming up with a scheme for the whole topic area than just doing this one merge. Have you had a look at List of political parties in Romania? Would you be open to changing this to a more general discussion, moving the discussion probably to the talk page of that article, and linking to the discussion from the Romanian Wikipedians' notice board? - Jmabel | Talk 06:56, 26 September 2006 (UTC)
 * Absolutely. I agree that the situation is not uniform enough at this point and that a unified, coordinated effort would be the most likely to achieve some sort of coherence. For the record, I also agree that the two PNŢ articles should be kept separate, perhaps with a section at the end of Article #1 and/or at the beginning of Article #2 describing what activity there was in the Romanian peasant movement, if not as a party then as an informal network of emigrés, between 1947 and 1990. Biruitorul 18:04, 26 September 2006 (UTC)
 * Sounds good to me. I have way too much on my plate right now to spearhead anything (even after a deliberate attempt at catch-up, I'm over 48 hours behind on my watchlist), but if someone decides to start a reorganization of the Romanian parties material, I will participate, and on the pre-Communist era I probably have a pretty good a set of reference materials at my disposal that are not online, though presumably not what someone will have with access to a good Romanian university library. - Jmabel | Talk

what does victim mean? Anonimu 21:15, 14 October 2006 (UTC)

 * It's a bit ambiguous. It can be anyone on the receiving end of harm. For example, the person against whom a crime is committed would be a "victim". It can, in some contexts, have a narrower meaning. Here, it seems to be used in a broad sense: presumably innocent people who received punishment at the hands of a government. - Jmabel | Talk 03:02, 18 October 2006 (UTC)
 * Heh, that's very subjective. A collectivized rich land owner could see himself as a victim, while the communists and the people with little or no land would consider the confiscation a right thing Anonimu 12:30, 18 October 2006 (UTC)

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On Their Political Position
Please, I respectfully request, that more research and investigation should be done on the issue of the political party's political position.

184.22.216.151 (talk) 23:25, 23 April 2018 (UTC)

Thank you to whomever updated this article. I appreciate it. 49.228.57.224 (talk) 16:06, 15 June 2020 (UTC)
 * Most welcome. Dahn (talk) 11:56, 5 December 2020 (UTC)

title: Talk:National Peasants' Party


text:
Talk:Rosemary Vodrey

Untitled
It's normally considered polite to explain a wholesale revert, if only because the User concerned may have spent some time on making the various edits. Could you explain why you did so in this case, especially in the light of Wikipedia advice on such actions? The main problem seems to be the dates; recent discussions on the subject indicated, I'd thought, broad agreement that it was inappropriate to link dates unless they were relevant; a list of notable things that happened on, say 3rd January, or in 1976, isn't relevant to most articles, including this one. I notice that I slipped on the link to Premier, so I understand that one.

There are a number of grammatical problems that need attending to, but there seems little point if you're going to revert the whole thing again, so I'd be grateful for a response. Mel Etitis ( Μελ Ετητης ) 23:21, 4 Feb 2005 (UTC)

My response:

I was unaware of any recent discussions concerning the use of dates in articles, and was puzzled by your decision to make the changes in question. If you could point me to the relevant discussions on this subject, I would be appreciative.

(Note also that corrections to grammatical errors will not be reverted.) CJCurrie 23:28, 4 Feb 2005 (UTC)

 * I'm afraid that I've lost track of the discussion, but I'll search for it as soon as the Wikipedia search function is up and running again. There were only a couple of problems left, which I've corrected). Mel Etitis ( Μελ Ετητης ) 23:36, 4 Feb 2005 (UTC)

 * Ah, I Googled and came up with this (which isn't what I originally saw, but is a more formal version of it). Mel Etitis ( Μελ Ετητης ) 23:39, 4 Feb 2005 (UTC)

Interesting ... I'd not seen that particular discussion before (though I was hardly shocked to discover that no official consensus had been reached, given wikipedia's history in such matters).

My own position on the matter is largely unchanged, however. From what I could tell, there were two primary reasons given against the linking of dates:

(i) Aesthetic merit. Having too many blue-links diminishes the visual quality of the page, apparently. (My response: I can understand why some would hold this opinion, though I myself do not share in it.)

(ii) Lack of practical value. Few people use the date-links, making them essentially superfluous. (My response: While I doubt that many wikipedia readers use them on a regular basis, some may. These links can inform people as to other world events which occurred at contemporaneous moments, and can assist in the creation of a larger "timeline".)

A further response: the date-links do no discernable harm to any reader. I can't see a compelling need to delete them, frankly.

I've incorporated date-links into all of the articles that I've written -- and, notwithstanding the objections of some users, I don't see a compelling need to stop.

On a separate note, thank you for correcting the silly "she"/"her" error which I made in haste about an house (I might have noticed it myself, but there's no guarantee of this).

On a further separate note, how does a professor of philosophy come to find interest in an obscure Canadian politician? CJCurrie 23:59, 4 Feb 2005 (UTC)

 * Ah, the glories of the random page function... (and don't stress the obscurity factor, or some officious person will come along and slap a VfD on the page on the grounds that she's a “nobody”. I've seen that too often, and I find it truly objectionable, especially when – no matter how obscure she is – she's probably done more, and affected more people, than all the ‘delete’-voters put together). Mel Etitis ( Μελ Ετητης ) 00:38, 5 Feb 2005 (UTC)

 * On that point, I couldn't agree more. And to be on the safe side:

 * Lest any pedantic vfd hound prowl these grounds, let it be known that Vodrey is obscure on the world stage, but locally significant. (And, anyway, the Wikipedia guidelines indicate that elected officials at the state level are unambiguously notable; in Canada, this would translate to provincial officials.)

 * My creation should be safe now ... CJCurrie 00:44, 5 Feb 2005 (UTC)

 * Oh, and I should apologise for my opening testiness; I probably shouldn't edit when I'm tired. Mel Etitis ( Μελ Ετητης ) 00:48, 5 Feb 2005 (UTC)

 * No offense taken. CJCurrie 00:50, 5 Feb 2005 (UTC)

title: Talk:Rosemary Vodrey


text:
International cricket in South Africa from 1971 to 1981

International cricket in South Africa between 1971 and 1981 consisted of four private tours arranged by English sports promoter Derrick Robins, two tours by a private team called the "International Wanderers", and one women's Test match. The apartheid policy followed by the South African Governments of the day meant that no Test match playing nation was willing to tour, thereby depriving world cricket of leading stars such as Graeme Pollock, Barry Richards, Clive Rice and Eddie Barlow.

The road to isolation
Sport in South Africa had been divided on racial lines since the early white settlers, and cricket was no different.

While Walter Read's Englishmen played against a non-white team, the Malays, in 1891-92, it would be 65 years before non-white South Africans played any other international cricket, with a team of Kenyan Asians touring against South African non-whites in 1956. However, with apartheid becoming ever stricter over time and being legally mandated in 1948, no non-white player was selected for the national Test team. This did not, however, stop white-majority Commonwealth nations from playing white South African teams at cricket.

The Basil D'Oliveira affair changed all that. D'Oliveira was a mixed-race South African (partly black – "coloured" under the Apartheid classification): as he was ineligible to play for his national side, he emigrated to England and played for them instead, going on tour to the West Indies in 1967. His performance on that tour was not impressive, and he was omitted from the Ashes Test squads in the following summer until the fifth and final Test at the Oval. He scored 158 in that Test, and was expected to make it to the team to tour South Africa in winter.

When initially he was not selected, there was great controversy in England, with D'Olivera being left in tears at the news, and English Test selectors and cricket officials being accused of pandering to the racism of the apartheid regime in South Africa. Then, when a vacancy became available after Tom Cartwright broke down during a County Cricket match, D'Oliveira was selected in his place. Upon hearing of this, South African Prime Minister John Vorster responded to his selection by saying that it was not a team of the Marylebone Cricket Club, but of the anti-apartheid Movement: England's tour was immediately cancelled.

However, Australia did tour in 1969/70, with the Proteas whitewashing them 4-0, making them de facto world champions of cricket. After this triumph, they did not play another official Test match for 22 years. Their tour to England was called off in 1970, with England hastily arranging a tour by a Rest of the World team which itself included three South Africans and South African-born Tony Greig (who represented England in Test cricket).

In September 1970, Garry Sobers, the West Indies' captain and their best cricketer caused controversy by playing in a double-wicket competition in Rhodesia. Although Sobers spent only 48 hours in Salisbury, he had time for a meal with the prime minister, Ian Smith, and described him as a great man to talk to.

Sobers' statement and his participation in the tournament caused backlash from Caribbean politicians who were vehemently opposed to apartheid and racism, with Guyanese prime minister Forbes Burnham saying Sobers was not welcome in his country until there was an apology, while the Jamaican government called for Sobers' resignation or ouster as captain, and the Indian prime minister, Indira Gandhi, barred the Indian cricket team from touring the West Indies until the matter was resolved.

While Sobers initially argued that he had done nothing wrong as he was a cricketer, not a politician, he ultimately apologised in October 1970 when the scandal threatened to break up the West Indies Cricket Board.

In the 1970s and 1980s, the South African Cricket Board ran a competition called the Howa Bowl, which was contested between non-white teams.

1971
South Africa tried to tour Australia in 1971, even going as far as suggesting that two black players, Dik Abed and Owen Williams were part of the team. Abed and Williams rejected the proposal. Also in 1971 Englishman Colin Cowdrey wanted to take a racially mixed team to South Africa and play separate black and white national teams. However, the coloured Board rejected the idea and persuaded Basil D'Oliveira to distance himself from it. Frank Waring, the Minister of Sport, declared that if cricketers from club level upwards declared that they were in favour of racially integrated cricket and their authorities, "Came to me and stated that this was the position, then I am fully prepared to take this matter to Cabinet".

On 3 May 1971 the Rest of South African XI and Currie Cup champions Transvaal walked off the field at Newlands to protest against the government's sports policies. Charles Fortune, renowned South African commentator, suggested that it would be best to walk off instead of refusing to play which would effect the support for their actions. Players for South Africa included Graeme Pollock (captain), Mike Procter, Vincent van der Bijl, Peter Pollock, Hylton Ackerman, Denis Lindsay, Graham Chevalier, Arthur Short and Andre Bruyns. Players for Transvaal included Barry Richards (guest player), Brian Bath, Clive Rice, Peter Carlstien and Don Mackay-Coghill (captain). Ali Bacher did not play because he was making up hours at the Baragwanath Hospital for time taken for cricket. Bacher’s South African team had beaten Australia 4—0 in their 1969/70 Test series.

In another attempt to receive a touring international side to visit, the South African Cricket Association invited New Zealand to play three matches against multiracial sides when they were en route to England. However, New Zealand declined the offer.

DH Robins’ XI January-February 1973
A women's Test team from New Zealand did visit South Africa at the start of 1972. In addition, Rhodesia, a country neighbouring South Africa that was also under White minority rule, attracted an International Wanderers side captained by England star Brian Close and that included nine Test players, one of whom was Basil D'Oliveira. They played just two games: a drawn game on 23-25 September 1972 and a 4-day match on 29 September-2 October 1972, which Rhodesia won easily by 411 runs, and did not tour South Africa. South African, Mike Procter, played for Rhodesia.

However the first "international" games played by South Africa post-isolation occurred after this. Derrick Robins, a millionaire businessman and chairman of Coventry City Football Club, had organised a number of private cricket tours in the past, arranged a tour to South Africa that took place between 1 January and 6 February 1973. His XI included many England Test players, who – unlike the 1981/2 South African tourists like Gooch and Underwood – did not suffer bans as a result of touring. Robins' aim was for his XI "to do so well that you will invite us back again". His players were also aware that England's Test selectors would notice how they performed.

There was some criticism of his decision to come to apartheid South Africa, which Robins dismissed by saying, "I do not want to answer political questions, but I'll say this: we are a team of English cricketers on a private tour, here to play anyone our hosts want us to play against." However, an attempt to mobilise opposition in England soon fizzled out.

The highlight of the tour was a 4-day game against a representative South African XI, the closest South Africa had come to choosing a Test squad since 1970. This game was changed to be the last one – highlighting that the tourists were treating their games seriously, rather than as a cricketing holiday. All the leading South African cricketers played, including many who had played Test matches before South Africa's expulsion from the world cricket community.

In this game DH Robins' XI won the toss and chose to field: that was a mistake as, courtesy of 100 runs from Barry Richards and 97 for Andre Bruyns, they piled on 387 runs. A strong all-round bowling performance saw DH Robins' XI get dismissed twice for under 160, with no player scoring more than 32, and the match end within 3 days. A 50 overs a side game was played on what would have been the fourth day. A tight match saw the South Africans edge home by one wicket.

DH Robins' XI team squad comprised: Tony Brown; David Brown; Frank Hayes; Jackie Hampshire; Robin Hobbs; David Hughes; Robin Jackman; Roger Knight; John Lever; Peter Lewington; Arnold Long; John Murray; Clive Radley; Mike Smith; David Turner; Peter Willey;  Bob Willis;

South African International XI (effectively a South African representative team) comprised: Ali Bacher (captain); Eddie Barlow; Andre Bruyns; Jackie du Preez; Lee Irvine; Donald Mackay-Coghill; Ken McEwan; Mike Procter; Barry Richards; Peter Swart. Additionally, Vintcent van der Bijl played in the one-day match, but not the 4-day match; Rupert Hanley played in the 4-day match, but not the one-day match.

DH Robins’ XI October-December 1973
At the start of the next South African season, Derrick Robins took another group of tourists to South Africa. Only Mike Smith and John Lever of those who toured earlier in 1973 went on this tour. Whilst the other players on the team were mostly English, there were also a number of players from other countries. Most notably the tour included Pakistani Younis Ahmed and West Indian John Shepherd. The other players in the touring squad were (English unless stated otherwise):

 * Brian Close (captain); Ray East; John Edrich; Bruce Francis (Australian); John Gleeson (Australian); Graham Johnson; Peter Lee; Graham Roope; John Snow; Roger Tolchard; Bob Woolmer (a South African, who was born in India and played for England)

After four warm-up games against the provinces, the tour included five games against fully representative South African sides, four of which were over 4 days, the other a one-day match over 50 overs. The one-day game was against an African XI in Soweto.

The South Africans who played in each of these representative squads were: Hylton Ackerman; Eddie Barlow (captain); Dassie Biggs; Lee Irvine; Graeme Pollock; Mike Procter; Barry Richards; Vintcent van der Bijl. Additionally, Peter Swart played in the 4-day games, but not the one-day game; Jackie du Preez and Anthony Smith just played in the first two 4-day games; Pelham Henwood and Rupert Hanley played in the third 4-day game and the one-day game; and Kevin Verdoorn only played in the one-day game.

The first of the representative games contained little of note, with slow scoring (South Africa's second innings of 287 took 112 overs) meant that it ended in a draw. The second game was dominated by two huge scores. John Edrich made 170 for DH Robins' XI, then Barry Richards made 180 for South Africa to ensure a second draw. The third and final first-class representative game started with South Africa winning the toss and putting DH Robins' XI into bat. DH Robins' XI only made 227 for 9 declared. The South African innings was dominated by 211 from Eddie Barlow and 125 from Lee Irvine as they piled on 528, with John Lever taking 6 for 117. A strong performance of 4 for 66 from Vintcent van der Bijl then helped South Africa dismiss DH Robins' XI for 218 to record a strong win in the match, and to take the three-match series 1-0.

The next day DH Robins' XI had their revenge in the only one-day game of the tour in a low scoring, but tight match.

DH Robins’ XI March-April 1975
Brian Close led a strong international team known as the "International Wanderers" to Rhodesia in September 1974. They played one game against Transvaal, but nothing else in South Africa. The Rhodesian team notably included South African-born Mike Procter, whilst the International Wanderers counted South African Eddie Barlow amongst their numbers. In the game against Transvaal in Johannesburg the international International Wanderers notably fielded two non-white players in their team, Barbadian John Shepherd and Pakistani Younis Ahmed. The three day match resulted in the International Wanderers beating Transvaal by 183 runs.

An Australian test team was scheduled to tour South Africa for the 1975-76 season. The tour was called off "with reluctance" according to Tim Caldwell, the chairman of the Australian Cricket Board. Australian Prime Minister Gough Whitlam stated that if Australia were to send a team to South Africa, it was likely that Australian sides would not be received in the Caribbean or Indian subcontinent and that teams from these countries may no longer visit Australia.

The next games for a representative South African side therefore took place on Derrick Robins third tour to South Africa in March and April 1975. This DH Robins' XI was again an international side. Captained once again by Brian Close, it included the following players from Robins' preceding tour: Bruce Francis (Australian), John Shepherd (West Indian), Roger Tolchard, Younis Ahmed (Pakistani). In addition, the following also toured: Malcolm Francke (Sri Lanka/Australia), Geoff Greenidge (West Indies), Tony Greig (South African-born England player), Jackie Hampshire, Frank Hayes, Eddie Hemmings, Terry Jenner (Australia), John Lyon, Clive Radley, Stephen Rouse, John Steele, Stuart Turner, Max Walker (Australia).

The South African Board President's XI was again captained by Eddie Barlow. It also, for the very first time in a South African representative match, included two black players. Edward Habane played in both the first-class match (the only one he ever played) and the one-dayer. Sedick Conrad played only in the first-class match. The other players were: Darryl Bestall, Simon Bezuidenhout, Rupert Hanley, Pelham Henwood, Lee Irvine, Graeme Pollock, Barry Richards, Vintcent van der Bijl. Also Peter Swart played in the one-day match, but not the first-class match.

The first-class match featuring the South African Board President's XI was dominated by an innings of 155 by South African legend, Eddie Barlow. DH Robins' XI was skittled out thanks to hauls of 5 for 41 from Pelham Henwood in the first innings, and 5 for 44 from Vintcent van der Bijl to leave the South Africans winners by 260 runs. More remarkable than the scores, however, was the inclusion of Edward Habane and Sedick Conrad, both black, in the South African squad. This was the first time coloured South Africans had played first-class cricket against a touring side since a South African Malays team played an English touring side in the 1890s.

The 40 over representative match was a low-scoring affair, with Barry Richards' 68 helping South Africa to a 5 wicket win with 6 balls to spare.

DH Robins’ XI January-February 1976
The International Wanderers made a three game tour to Rhodesia in September and October 1975, but other than that there was no international cricket in Southern Africa until a tour by another DH Robins' XI in January and February 1976. However, only one game of this tour, a 60 over affair, was played against a representative South African XI as the main games for South Africa would come slightly later in the season against another International Wanderers team.

The members of touring party were (England unless stated): Phil Carrick, Trevor Chappell (Australia), Geoff Cope, John Douglas (Australia), Frank Hayes, Mike Hendrick, Geoff Howarth (New Zealand), Andrew Kennedy, Peter Lee, David Lloyd (captain), Derek Randall, Phil Slocombe, David Steele, Fred Titmus, Roger Tolchard, Gary Troup (New Zealand), Dav Whatmore (Australia).

The South African Invitation XI was again captained by Eddie Barlow. It also included one black cricketer, Samson Sonwabe. The other players were David Dyer, Rupert Hanley, Denys Hobson, Lee Irvine, Graeme Pollock, Clive Rice, Barry Richards, Anthony Smith and Vintcent van der Bijl.

The representative match was low and slow scoring, with South Africa making 219-7 in their 60 overs. The highlights were half centuries from Dyer, Pollock and Richards and 4 for 28 from Troup. DH Robins' XI struggled in reply, collapsing from 125-3 to 164 all out with no player reaching his half century.

International Wanderers March-April 1976
The highlight of the South African 1975/6 season was a tour by the International Wanderers. They played 3 first-class games and 1 one-day game against a South African Invitation XI. They also played a first-class game against a weaker South African Board President's XI. This was the strongest team to tour South Africa since isolation, and comprised players from 4 countries. The tourists were managed by Richie Benaud and captained by Australian Greg Chappell in all four main representative games. Englishmen Mike Denness and Bob Taylor, and West Indian John Shepherd also played in all four games. The other players, their nationalities and the games they played in are as follows (numbers relate to the first-class games, OD relates to the one-day game): Ian Chappell (Australia) 1, OD; Phil Edmonds (Zambian-born Englishman) OD, 3; Gary Gilmour (Australia) 1, 2, 3; Alan Hurst (Australia) 1, 3; Martin Kent (Australia) 1, 2, 3; Dennis Lillee (Australia) 2, 3; Ashley Mallett (Australia) 1, OD, 2; John Morrison (New Zealand) 1, OD, 2; Glenn Turner (New Zealand) OD, 2, 3; Derek Underwood (England) 1, OD, 3; Max Walker (Australia) OD, 2.

The South African Invitation XI was again captained by Eddie Barlow, who played in all four representative games, as did Clive Rice and Vintcent van der Bijl. A number of coloured players were selected for the Invitation XI. These, and the games they played in, were Abdullatief Barnes 1, 2; Winston Carelse 1, 2; Ismail Ebrahim 3; Devdas Govindjee OD; D Jacobs OD; Farouk Timol 3.

The other players selected for South Africa were Hylton Ackerman OD; Howard Bergins 1, 2, 3; Henry Fotheringham 1; Jack Heron 1; Denys Hobson 1; Lee Irvine OD, 2, 3; Peter Kirsten 1; Douglas Neilson OD; Gavin Pfuhl 1; Graeme Pollock OD, 2, 3; Anthony Smith OD, 2, 3; Barry Richards OD, 2, 3; Lorrie Wilmot 2, 3.

The end of international tours
During the early to mid-1970s there had been various attempts by the different South African cricket bodies representing the whites, coloureds and black to play multiracial cricket despite Government opposition. In June 1976, however, there were major political uprisings in South Africa. The main outbreak of civil strife was the Soweto Uprising, centred on Soweto, the black township attached to Johannesburg. On 16 June, thousands of schoolchildren rebelled against the education policy of the white minority government. Hundreds were killed; US newspaper Newsday estimated 332 had died in Soweto and 435 nationally. Many others went into exile.

On 17 July 1976 the Montréal Olympics opened without 25 African countries (later joined by 4 others) who were boycotting the games as a result of New Zealand retaining sporting ties with South Africa – the New Zealand rugby union team were touring South Africa at the time.

In the light of this political strife, new changes were proposed, which included the placing of a moratorium on tours to and from South Africa. In practice no international tour happened until the first of the South African rebel tours in 1982.


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Chesty Morgan

Ilana Wajc (born October 15, 1937), better known by her stage name Chesty Morgan, and also known as Liliana Wilczkowska and Lillian Stello, is a Polish-born, retired exotic dancer of Jewish descent, who also starred in two films directed by Doris Wishman. Morgan was billed as having a 73 in bust measurement.

Early life
As a young girl growing up near Warsaw, Poland, she was orphaned when her Jewish parents were killed by the Nazis after the Invasion of Poland. Sent to Israel, she lived in a series of orphanages before ending up in a kibbutz.

Career
Following moving to the United States in the late 1950s, and the death of her husband in 1965, Morgan began her career as a stripper in the early 1970s, using the name Zsa Zsa. A nightclub owner suggested she call herself "Chesty Morgan". She never stripped below the waist, and in traditional burlesque fashion, valued the tease as much as the strip. She was occasionally arrested, allegedly for letting men near the stage touch the tops of her breasts to verify that they were real.

Unlike many of the modern adult entertainment stars with large breasts, Morgan's were not augmented with implants. According to the 1988 edition of Guinness Movie Facts & Feats, her bust measurement is the largest on record for a film star.

She starred in two Doris Wishman films in 1974: Deadly Weapons and Double Agent 73. She was also filmed by Federico Fellini as Barbarina in Fellini's Casanova, but her scenes were cut. Clips from Doris Wishman's two 1970s sexploitation films, based around Morgan's very large breasts, were featured in John Waters' 1994 film, Serial Mom. Waters also wrote a role for Morgan in his never-made feature Flamingos Forever.

Personal life
In 1957, Morgan married an American, Josef Wilczkowski, and moved to New York. Wilczkowski was killed in a Brooklyn robbery in 1965, when she was 27, and her two daughters, Eva and Lila, were four years old and four months old, respectively. In 1974, Morgan married National League baseball umpire Dick Stello. The two divorced in 1979, but remained friends until Stello's death in a traffic accident in 1987. In 1984, her elder daughter Eva was also killed in a traffic accident.

Retirement
Morgan's last performance as a stripper was in Houston on the first night of the Persian Gulf War in 1991. Since her retirement, she has lived in Tampa Bay, Florida.

title: Chesty Morgan


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User talk:Andrewa/wisecracks

This is a page on which I'll put some (original unless marked) wisecracks to relieve the tension or monotony of discussions. Please don't edit it or this page, instead set up your own or a shared page if you want to add to or improve the quotes, and let's have any discussions on my main talk page where I'll find them more easily. TIA. Andrewa 23:23, 4 Feb 2005 (UTC)

title: User talk:Andrewa/wisecracks


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User:LiquidFox

Please do not make pointless edits.

title: User:LiquidFox


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Wikipedia:Articles for deletion/Nikonian

 This page is an archive of the discussion about the proposed deletion of the article below. This page is no longer live. Further comments should be made on the article's talk page rather than here so that this page is preserved as an historic record. The result of the debate was NO CONSENSUS.

The votes were 3 keep, 3 delete. I didn't count Paul Fischer, since his vote was his first contribution. dbenbenn | talk 22:44, 10 Feb 2005 (UTC)

Nikonian
Non-notable forum. Linking to the webpage three times in a one-paragraph article is a sign of vanity. RickK 23:24, Feb 4, 2005 (UTC)
 * Delete, website advertisement, neologism, article as it stands is un-encyclopaedic. Megan1967 02:13, 5 Feb 2005 (UTC)
 * Retain, word is in fairly common use on internet photography sites (not just nikonians.org). Article has been edited to make it more encyclopedic.--Paul Fisher 03:12, 5 Feb 2005 (UTC)
 * Keep, first impression is a complete yawn, but this article describes a popular and helpful website. Wyss 22:24, 5 Feb 2005 (UTC)
 * keep. Yuckfoo 01:21, 6 Feb 2005 (UTC)
 * Keep, looks notable. Bart133 (t) 02:12, 9 Feb 2005 (UTC)
 * Delete Should have an entry in wikidictionary plus the website is supported by Nikon max rspct 23:11, 9 Feb 2005 (UTC)

This page is now preserved as an archive of the debate and, like some other VfD subpages, is no longer 'live'. Subsequent comments on the issue, the deletion, or the decision-making process should be placed on the relevant 'live' pages. Please do not edit this page.


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User:Alasseo

WP:COPYARTICLE, old copy of Eagle Ridge Academy

title: User:Alasseo


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White Witch (DC Comics)

White Witch (Mysa Nal, originally Xola Aq) is a fictional character appearing in media published by DC Comics. Created by E. Nelson Bridwell and Curt Swan, she is usually depicted as a member of the Legion of Super-Heroes in the 30th and 31st centuries. She is the sister of fellow Legionnaire Dream Girl and daughter of Kiwa Nal, the former High Seer of Naltor. Like Dream Girl, she is a native of the planet Naltor, where nearly everyone has the power of precognition, but unlike most Naltorians, Mysa cannot foresee the future.

Fictional character biography
To compensate for her inability to see the future, Mysa trained in the mystic arts on the planet Zerox, known as the 'Sorcerer's World', under the tutelage of five instructors (each having their own specialty - Air, Earth, Fire, Light and Water) and became an accomplished sorceress instead. Mysa showed a remarkable aptitude for magic and easily excelled in her studies — much to the chagrin of the envious Mordru. Originally, she had red hair, but as she trained in magic, her hair and skin became chalk white and her eyes bright red. This change happened gradually after Dream Girl freed her from the "Hag" guise.

She first appeared in Adventure Comics #350 as the Hag, an apparently ancient magic user and an agent of the villainous Prince Evillo. When the Legion fought Evillo, two mysterious "new" members, "Sir Prize" and "Miss Terious" (actually Star Boy and Dream Girl) cast a spell that restored her to her true form. It was later revealed that this transformation had been worked by the villainous wizard Mordru.

She joined the Legion after helping them defeat Darkseid in the famous Legion story, the Great Darkness Saga. Mysa proved herself a valuable member, often coming to member's aid with a handy spell or two. One feature that set the White Witch apart from the typical comic book sorcerer was a specific limitation on her spell-casting ability; she could only memorize a few spells at a time. Unlike characters like Dr. Fate, Mysa required study before casting a spell.

The White Witch played a prominent part in the so-called "Magic Wars", which concluded Legion of Super-Heroes (vol. 3).

Some years later, after leaving the Legion, she married the presumedly-reformed Mordru and lived with him on the planet Tharn, which was, at that point, subdued and invaded by Mordru's magics. She was subjected to mystical imprisonment and manipulation during this period until the Legionnaires returned looking for her and their comrade Rond Vidar. Mysa was also a physical vessel for the disembodied soul of Amethyst, one of the Lords of Order who is currently active in the present day DC Universe. It was this incarnation of the Legion's near defeat that led Mysa to take up arms against her husband, and she later rejoined the group. Right before Zero Hour, she was de-aged by Glorith to a teenager and appeared happy with the change. She assumed the codename Jewel and went underground with her fellow Legionnaires.

Reboot version
In post-Zero Hour continuity, Mysa was no longer Dream Girl's sister from Naltor, but rather, the daughter of Mordru.

The only survivor of a group of sorcerers who imprisoned Mordru, she spent a century preparing for his return, including planting the seeds for Zoe Saugin's powers and manipulating much of the girl's life to make her an ally against Mordru's next rise. After Mordru rose again, Mysa (who resembled the pre-Zero Hour Hag at this point) was reverted to the age at which she first defeated him and helped the Legion imprison him once more.

Mysa settled on Sorcerer's World and fell in love with Dragonmage.

Threeboot version
In the "Threeboot" continuity, White Witch has appeared as a member of Mekt Ranzz's Wanderers. Her home planet is listed as "unknown".

Post-Infinite Crisis
In Superman and the Legion of Super-Heroes story arc, featuring a group of Legionnaires based on the original, pre-Crisis incarnation, Spider Girl traded Mysa to Mordru in return for not attacking Earth. At the conclusion of the story, Wildfire comments to Superman that Dawnstar has a lock on Mysa's location, while Chameleon Girl assures Superman that the Legion will find their remaining lost teammates.

In the Legion of Three Worlds limited series, the White Witch is imprisoned on Sorcerer's World by Mordru until she is freed by members of the Legion, including Blok. It is revealed at this point that Blok and Mysa are in a relationship. Their escape, however, is thwarted by Mordru, and then Superboy-Prime's Legion of Super-Villains. Mysa uses Dawnstar's tracking ability to open a portal directly to Legion headquarters. Fellow Legionnaire, Green Lantern Rond Vidar, forces his teammates through the portal to prevent the LSV from following. Back at Legion headquarters, Mysa attempts another portal to rescue Rond but is too late as he is killed by Superboy-Prime.

Brainiac 5 then enlists the White Witch to cast a seance spell on an old Justice League space-time crystal ball to bring the "Reboot" and "Threeboot" Legions to aid in their battle against Superboy-Prime.

In the midst of battle, "Reboot" Legionnaire Kinetix, who possesses magic-based powers, is killed by Superboy-Prime while Mordru absorbs her life-force and all of her magical powers. Because her home reality was destroyed during the events of Infinite Crisis, Kinetix also possessed all of that universe's magic energies, now passed on to Mordru. Mordru began using his vastly increased powers in the villains' favor and launches a brutal attack on Blok to draw out Mysa. She reluctantly attacks Mordru with one of his own dark spells that allows her to steal his life-force and magics in a bright blaze of light. Mysa re-emerges as the Black Witch with a black costume and hair, using her increased powers to defeat most of the villains single-handedly.

At the conclusion of the story, the Black Witch remains a member of the Legion. However, Blok senses great trouble with his love's transformation. His concern increases as she returns to Sorcerer's World and claims Mordru's throne, vowing a vigilance against evil.

Later, Blok again reaches the Sorcerers' World, only to find the Black Witch sitting on a throne in front of several spellcasters imprisoned in the stone behind her. Poking out of the wall are the faces of Alan Scott, the Green Lantern wizard Torquemada, Blue Devil, Zatanna, Raven and Kid Devil. Later, both she and Blok cement their relationship, hoping to use Mordru's dark powers for the good of the planet.

Powers and abilities
Mysa Nal was trained by the master magician, Mordru. She can cast a variety of magic spells, such as creating force fields, transmuting matter, absorbing energy, and generating dimensional portals, among other feats. The only drawback is her memory, plus an additional time-consuming preparation for them, which could take up from minutes to hours. As the White Witch, Mysa possesses expertise in occultism.

Equipment
As a member of the Legion of Super-Heroes, she is provided her own Legion Flight Ring. It allows her to fly and survive in the vacuum of space and other dangerous environments.

In other media

 * The White Witch appears in the Legion of Super Heroes episode "Trials", voiced by Lauren Tom. This version is not a member of the Legion of Super-Heroes and leader of the trials that banished wizards of Zerox can undergo to regain their magic.
 * The White Witch appears in Legion of Super Heroes in the 31st Century #18.

Reception
Jesse Murray of Syfy placed Mysa Nal as the 22nd greatest Legion of Super-Heroes member of all time, noting her relationship drama with a "big-baddie" of the superhero team Mordru and calling her moment of her absorbing his powers as the Black Witch as one of the defining moments for her. Eileen Gonzalez of Comic Book Resources placed her as one of the "best" Legion superheroes out both a best and worst character list. Eileen noted her pivotal roles in "The Great Darkness Saga" with her role of stopping Darkseid and once again the role of "Final Crisis" stopping Mordru as defining moments as well. Caleb Bailey of Comic Book Resources placed her and her powers as a "powerful magic user who could probably give Zatanna a run for her top hat".

title: White Witch (DC Comics)


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User talk:Vrubinstein

Welcome, and Haifa
Hi there, and welcome to Wikipedia!

Your contribution at Haifa Through My Eyes has been nominated for deletion by UncleG. This is nothing personal, against you, against the good city of Haifa, etc. I'm an inclusionist, in favour of including many articles others (like "deletionists") would want to delete. But I agree with UncleG here, and I think everybody will.

The problem is that Wikipedia isn't just everything we want to put up - Wikipedia is a project to write and organize information the way an encyclopedia would write and organize information. For one thing, you wouldn't expect to look up the title "Haifa Through My Eyes" in an encyclopedia. Also, it expresses your opinion about Haifa, and is written as if it comes from one author. Once we submit something to Wikipedia, it should be ready for other people to change around at will. From the moment we contribute something here, it's not entirely from you or me - in a way, it's from every Wikipedian.

So I'd like to suggest three things:

 * If you went back to edit Haifa Through My Eyes and deleted what you had written there (please do save it on your own computer), we could wrap up the time-consuming Votes for deletion process quickly, and everybody involved would be happy.

Then:

 * Go to Haifa, get a sense for how that article is written and what it includes, and if there are relevant additions you could make in the same sort of style, please add away!
 * Also, you might like to join the parallel project at Wikitravel.org. It's run by different people and it uses a different copyright license, so you can't just cut and paste from Wikipedia to Wikitravel, unless you're contributing there something you've written here yourself. Wikitravel is the travel guide Wiki, and they have an article on Haifa that could use expansion. Take a look at Jerusalem to see how it's done.

Comments or questions? Feel free to respond on my talk page.

Cheers! Samaritan 23:25, 4 Feb 2005 (UTC)

Haifa
I've deleted Haifa Through My Eyes from the article namespace and left a copy at User:Vrubinstein/Haifa_Through_My_Eyes for your convenience. Happy editing. Mgm|(talk) 09:40, Feb 10, 2005 (UTC)

title: User talk:Vrubinstein


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User talk:Finnefrock

Hi,

I'm Adam Finnefrock. I do research on HIV, specifically HIV vaccines, at Merck & Co.. I live in Tredyffrin Township, Pennsylvania, not far from Valley Forge.

title: User talk:Finnefrock