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Limit of a function

Although the function $\tfrac{\sin x}{x}$ is not defined at zero, as $x$ becomes closer and closer to zero, $\tfrac{\sin x}{x}$ becomes arbitrarily close to 1. In other words, the limit of $\tfrac{\sin x}{x},$ as $x$ approaches zero, equals 1.

In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input which may or may not be in the domain of the function.

Formal definitions, first devised in the early 19th century, are given below. Informally, a function $f$ assigns an output $f(x)$ to every input $x$. We say that the function has a limit $L$ at an input $p$, if $f(x)$ gets closer and closer to $L$ as $x$ moves closer and closer to $p$. More specifically, the output value can be made arbitrarily close to $L$ if the input to $f$ is taken sufficiently close to $p$. On the other hand, if some inputs very close to $p$ are taken to outputs that stay a fixed distance apart, then we say the limit does not exist.

The notion of a limit has many applications in modern calculus. In particular, the many definitions of continuity employ the concept of limit: roughly, a function is continuous if all of its limits agree with the values of the function. The concept of limit also appears in the definition of the derivative: in the calculus of one variable, this is the limiting value of the slope of secant lines to the graph of a function.

History
Although implicit in the development of calculus of the 17th and 18th centuries, the modern idea of the limit of a function goes back to Bolzano who, in 1817, introduced the basics of the epsilon-delta technique (see (ε, δ)-definition of limit below) to define continuous functions. However, his work was not known during his lifetime.

In his 1821 book Cours d'analyse, Augustin-Louis Cauchy discussed variable quantities, infinitesimals and limits, and defined continuity of $$y=f(x)$$ by saying that an infinitesimal change in $x$ necessarily produces an infinitesimal change in $y$, while Grabiner claims that he used a rigorous epsilon-delta definition in proofs. In 1861, Weierstrass first introduced the epsilon-delta definition of limit in the form it is usually written today. He also introduced the notations $\lim$ and $\textstyle \lim_{x \to x_0} \displaystyle.$

The modern notation of placing the arrow below the limit symbol is due to Hardy, which is introduced in his book A Course of Pure Mathematics in 1908.

Motivation
Imagine a person walking on a landscape represented by the graph $y = f(x)$. Their horizontal position is given by $x$, much like the position given by a map of the land or by a global positioning system. Their altitude is given by the coordinate $y$. Suppose they walk towards a position $x = p$, as they get closer and closer to this point, they will notice that their altitude approaches a specific value $L$. If asked about the altitude corresponding to $x = p$, they would reply by saying $y = L$.

What, then, does it mean to say, their altitude is approaching $L$? It means that their altitude gets nearer and nearer to $L$—except for a possible small error in accuracy. For example, suppose we set a particular accuracy goal for our traveler: they must get within ten meters of $L$. They report back that indeed, they can get within ten vertical meters of $L$, arguing that as long as they are within fifty horizontal meters of $p$, their altitude is always within ten meters of $L$.

The accuracy goal is then changed: can they get within one vertical meter? Yes, supposing that they are able to move within five horizontal meters of $p$, their altitude will always remain within one meter from the target altitude $L$. Summarizing the aforementioned concept we can say that the traveler's altitude approaches $L$ as their horizontal position approaches $p$, so as to say that for every target accuracy goal, however small it may be, there is some neighbourhood of $p$ where all (not just some) altitudes correspond to all the horizontal positions, except maybe the horizontal position $p$ itself, in that neighbourhood fulfill that accuracy goal.

The initial informal statement can now be explicated:

In fact, this explicit statement is quite close to the formal definition of the limit of a function, with values in a topological space.

More specifically, to say that

$$ \lim_{x \to p}f(x) = L,$$

is to say that $f(x)$ can be made as close to $x$ as desired, by making $p$ close enough, but not equal, to $L$.

The following definitions, known as $f(x)$-definitions, are the generally accepted definitions for the limit of a function in various contexts.

$f(x)$-definition of limit
Suppose $$f: \R \rightarrow \R$$ is a function defined on the real line, and there are two real numbers $L$ and $p$. One would say that the limit of $L$, as $x$ approaches $p$, is $f$ and written

$$ \lim_{x \to p} f(x) = L,$$

or alternatively, say $(ε, δ)$ tends to $a$ as $b$ tends to $x$, and written:

$$ f(x) \to L \text{ as } x \to p,$$

if the following property holds: for every real $(ε, δ)$, there exists a real $f(x)$ such that for all real $p$, $(b – ε, b + ε)$ implies $(a – δ, a + δ).$. Symbolically, $$(\forall \varepsilon > 0 ) \, (\exists \delta > 0) \, (\forall x \in \R) \, (0 < |x - p| < \delta \implies |f(x) - L| < \varepsilon).$$

For example, we may say $$\lim_{x \to 2} (4x + 1) = 9$$ because for every real $f(x) → b$, we can take $x → a$, so that for all real $L$, if $f(x)$, then $ε > 0$.

A more general definition applies for functions defined on subsets of the real line. Let $f$ be a subset of $x$ Let $$f: S \to \R$$ be a real-valued function. Let $p$ be a point such that there exists some open interval $δ > 0$ containing $L$ with $$(a,p)\cup (p,b) \subset S.$$ It is then said that the limit of $L$ as $x$ approaches $p$ is $x$, if:

Or, symbolically: $$(\forall \varepsilon > 0 ) \, (\exists \delta > 0) \, (\forall x \in (a, b)) \, (0 < |x - p| < \delta \implies |f(x) - L| < \varepsilon).$$

For example, we may say $$\lim_{x \to 1} \sqrt{x+3} = 2$$ because for every real $0 < |x − p| < δ$, we can take $|f(x) − L| < ε$, so that for all real $ε > 0$, if $δ = ε/4$, then $0 < |x − 2| < δ$. In this example, $|4x + 1 − 9| < ε$ contains open intervals around the point 1 (for example, the interval (0, 2)).

Here, note that the value of the limit does not depend on $x$ being defined at $S$, nor on the value $(a, b)$—if it is defined. For example, let $$f: [0,1)\cup (1,2] \to \R, f(x) = \tfrac{2x^2 - x - 1}{x-1}.$$ $$\lim_{x \to 1} f(x) = 3$$ because for every $ε > 0$, we can take $δ > 0$, so that for all real $x ∈ (a, b)$, if $0 < |x − p| < δ$, then $|f(x) − L| < ε$. Note that here $ε > 0$ is undefined.

In fact, a limit can exist in $$\{x\in \R\, |\, \exists (a,b) \subset \R \quad p \in (a,b) \text{ and } (a,p)\cup (p, b) \subset S\},$$ which equals $$\operatorname{int} S \cup \operatorname{iso} S^c,$$ where $δ = ε$ is the interior of $\R.$, and $x ≥ −3$ are the isolated points of the complement of $p$. In our previous example where $$S = [0,1) \cup (1,2],$$ $$\operatorname{int} S = (0,1) \cup (1,2),$$ $$\operatorname{iso} S^c = \{1\}.$$ We see, specifically, this definition of limit allows a limit to exist at 1, but not 0 or 2.

The letters $p$ and $f$ can be understood as "error" and "distance". In fact, Cauchy used $x$ as an abbreviation for "error" in some of his work, though in his definition of continuity, he used an infinitesimal $$\alpha$$ rather than either $p$ or $L$ (see Cours d'Analyse). In these terms, the error (ε) in the measurement of the value at the limit can be made as small as desired, by reducing the distance (δ) to the limit point. As discussed below, this definition also works for functions in a more general context. The idea that $f$ and $p$ represent distances helps suggest these generalizations.

Existence and one-sided limits

Alternatively, $S$ may approach $S$ from above (right) or below (left), in which case the limits may be written as

$$ \lim_{x \to p^+}f(x) = L $$

or

$$ \lim_{x \to p^-}f(x) = L $$ respectively. If these limits exist at p and are equal there, then this can be referred to as the limit of $0 < |x − 1| < δ$ at $ε$. If the one-sided limits exist at $δ$, but are unequal, then there is no limit at $ε$ (i.e., the limit at $ε$ does not exist). If either one-sided limit does not exist at $δ$, then the limit at $δ$ also does not exist.

A formal definition is as follows. The limit of $ε$ as $x$ approaches $p$ from above is $p$ if:
 * For every $|f(x) − 2| < ε$, there exists a $S = [−3, ∞)$ such that whenever $f(p)$, we have $ε > 0$.

$$(\forall \varepsilon > 0 ) \, (\exists \delta > 0) \, (\forall x \in (a,b))\, (0 < x - p < \delta \implies |f(x) - L| < \varepsilon).$$

The limit of $p$ as $p$ approaches $p$ from below is $p$ if:
 * For every $δ = ε/2$, there exists a $x ≠ 1$ such that whenever $0 < |x − 1| < δ$, we have $|f(x) − 3| < ε$.

$$(\forall \varepsilon > 0 )\, (\exists \delta > 0) \, (\forall x \in (a,b)) \, (0 < p - x < \delta \implies |f(x) - L| < \varepsilon).$$

If the limit does not exist, then the oscillation of $p$ at $f$ is non-zero.

More general definition using limit points and subsets
Limits can also be defined by approaching from subsets of the domain.

In general: Let $$f : S \to \R$$ be a real-valued function defined on some $$S \subseteq \R.$$ Let $x$ be a limit point of some $$T \subset S$$—that is, $p$ is the limit of some sequence of elements of $L$ distinct from $f$. Then we say the limit of $x$, as $p$ approaches $L$ from values in $f$, is $p$, written $$\lim_{ {x \to p} \atop {x \in T} } f(x) = L$$ if the following holds:

$$(\forall \varepsilon > 0 )\, (\exists \delta > 0) \,(\forall x \in T)\, (0 < |x - p| < \delta \implies |f(x) - L| < \varepsilon).$$

Note, $p$ can be any subset of $p$, the domain of $T$. And the limit might depend on the selection of $p$. This generalization includes as special cases limits on an interval, as well as left-handed limits of real-valued functions (e.g., by taking $f$ to be an open interval of the form $f(1)$), and right-handed limits (e.g., by taking $x$ to be an open interval of the form $int S$). It also extends the notion of one-sided limits to the included endpoints of (half-)closed intervals, so the square root function $$f(x) = \sqrt x$$ can have limit 0 as $p$ approaches 0 from above: $$\lim_{ {x\to 0} \atop {x\in [0, \infty)} } \sqrt{x} = 0$$ since for every $iso Sc$, we may take $x → x_{0}$ such that for all $f(x)$, if $ε > 0$, then $δ > 0$.

This definition allows a limit to be defined at limit points of the domain $T$, if a suitable subset $L$ which has the same limit point is chosen.

Notably, the previous two-sided definition works on $$\operatorname{int} S \cup \operatorname{iso} S^c,$$ which is a subset of the limit points of $T$.

For example, let $$S = [0,1)\cup (1, 2].$$ The previous two-sided definition would work at $$1 \in \operatorname{iso} S^c = \{1\},$$ but it wouldn't work at 0 or 2, which are limit points of $S$.

Deleted versus non-deleted limits
The definition of limit given here does not depend on how (or whether) $f$ is defined at $T$. Bartle refers to this as a deleted limit, because it excludes the value of $T$ at $T$. The corresponding non-deleted limit does depend on the value of $x$ at $S$, if $T$ is in the domain of $S$. Let $$f : S \to \R$$ be a real-valued function. The non-deleted limit of $S$, as $f$ approaches $p$, is $f$ if

$$(\forall \varepsilon > 0 )\, (\exists \delta > 0) \, (\forall x \in S)\, (|x - p| < \delta \implies |f(x) - L| < \varepsilon).$$

The definition is the same, except that the neighborhood $0 < x − p < δ$ now includes the point $p$, in contrast to the deleted neighborhood $|f(x) − L| < ε$. This makes the definition of a non-deleted limit less general. One of the advantages of working with non-deleted limits is that they allow to state the theorem about limits of compositions without any constraints on the functions (other than the existence of their non-deleted limits).

Bartle notes that although by "limit" some authors do mean this non-deleted limit, deleted limits are the most popular.

Non-existence of one-sided limit(s)
The function $$f(x)=\begin{cases} \sin\frac{5}{x-1} & \text{ for } x<1 \\ 0 & \text{ for } x=1 \\[2pt] \frac{1}{10x-10}& \text{ for } x>1 \end{cases}$$ has no limit at $ε > 0$ (the left-hand limit does not exist due to the oscillatory nature of the sine function, and the right-hand limit does not exist due to the asymptotic behaviour of the reciprocal function, see picture), but has a limit at every other $f$-coordinate.

The function $$f(x)=\begin{cases} 1 & x \text{ rational } \\ 0 & x \text{ irrational } \end{cases}$$ (a.k.a., the Dirichlet function) has no limit at any $p$-coordinate.

Non-equality of one-sided limits
The function $$f(x)=\begin{cases} 1 & \text{ for } x < 0 \\ 2 & \text{ for } x \ge 0 \end{cases}$$ has a limit at every non-zero $p$-coordinate (the limit equals 1 for negative $f$ and equals 2 for positive $f$). The limit at $δ > 0$ does not exist (the left-hand limit equals 1, whereas the right-hand limit equals 2).

Limits at only one point
The functions $$f(x)=\begin{cases} x & x \text{ rational } \\ 0 & x \text{ irrational } \end{cases}$$ and $$f(x)=\begin{cases} 0 & x \text{ irrational } \end{cases}$$ both have a limit at $0 < p − x < δ$ and it equals 0.
 * x| & x \text{ rational } \\

Limits at countably many points
The function $$f(x)=\begin{cases} \sin x & x \text{ irrational } \\ 1    &  x \text{ rational } \end{cases}$$ has a limit at any $x$-coordinate of the form $$\tfrac{\pi}{2} + 2n\pi,$$ where $p$ is any integer.

Limits at infinity

Let $$f:S \to \R$$ be a function defined on $$S \subseteq \R.$$ The limit of $L$ as $p$ approaches infinity is $x$, denoted

$$ \lim_{x \to \infty}f(x) = L,$$

means that:

$$(\forall \varepsilon > 0 )\, (\exists c > 0) \,(\forall x \in S) \,(x > c \implies |f(x) - L| < \varepsilon).$$

Similarly, the limit of $x$ as $x$ approaches minus infinity is $x$, denoted

$$ \lim_{x \to -\infty}f(x) = L,$$

means that:

$$(\forall \varepsilon > 0)\, (\exists c > 0) \,(\forall x \in S)\, (x < -c \implies |f(x) - L| < \varepsilon).$$

For example, $$ \lim_{x \to \infty} \left(-\frac{3\sin x}{x} + 4\right) = 4$$ because for every $|f(x) − L| < ε$, we can take $ε > 0$ such that for all real $x$, if $δ > 0$, then $x ∈ T$.

Another example is that $$ \lim_{x \to -\infty}e^{x} = 0$$ because for every $0 < |x − p| < δ$, we can take $|f(x) − L| < ε$ such that for all real $x$, if $(–∞, a)$, then $(a, ∞)$.

Infinite limits
For a function whose values grow without bound, the function diverges and the usual limit does not exist. However, in this case one may introduce limits with infinite values.

Let $$f:S \to\mathbb{R}$$ be a function defined on $$S\subseteq\mathbb{R}.$$ The statement the limit of $n$ as $f$ approaches $x$ is infinity, denoted

$$ \lim_{x \to p} f(x) = \infty, $$

means that:

$$(\forall N > 0)\, (\exists \delta > 0)\, (\forall x \in S)\, (0 < | x-p | < \delta \implies f(x) > N) .$$

The statement the limit of $L$ as $f$ approaches $x$ is minus infinity, denoted

$$ \lim_{x \to p} f(x) = -\infty, $$

means that:

$$(\forall N > 0) \, (\exists \delta > 0) \, (\forall x \in S)\, (0 < | x-p | < \delta \implies f(x) < -N) .$$

For example, $$\lim_{x \to 1} \frac{1}{(x-1)^2} = \infty$$ because for every $ε > 0$, we can take $\delta = \tfrac{1}{\sqrt{N}\delta} = \tfrac{1}{\sqrt N}$  such that for all real $δ = ε$, if $x ≥ 0$, then $0 < |x − 0| < δ$.

These ideas can be used together to produce definitions for different combinations, such as

$$ \lim_{x \to \infty} f(x) = \infty,$$ or $$ \lim_{x \to p^+}f(x) = -\infty.$$

For example, $$\lim_{x \to 0^+} \ln x = -\infty$$ because for every $|f(x) − 0| < ε$, we can take $ε > 0$ such that for all real $δ > 0$, if $x ∈ S$, then $|x − p| < δ$.

Limits involving infinity are connected with the concept of asymptotes.

These notions of a limit attempt to provide a metric space interpretation to limits at infinity. In fact, they are consistent with the topological space definition of limit if In this case, $L$ is a topological space and any function of the form $$f : X \to Y$$ with $$X, Y \subseteq \overline \R$$ is subject to the topological definition of a limit. Note that with this topological definition, it is easy to define infinite limits at finite points, which have not been defined above in the metric sense.
 * a neighborhood of −∞ is defined to contain an interval $|f(x) − L| < ε$ for some $x$
 * a neighborhood of ∞ is defined to contain an interval $|x − p| < δ$ where $x$ and
 * a neighborhood of $f$ is defined in the normal way metric space $x$

Alternative notation
Many authors allow for the projectively extended real line to be used as a way to include infinite values as well as extended real line. With this notation, the extended real line is given as $p$ and the projectively extended real line is $f$ where a neighborhood of ∞ is a set of the form $$\{x: |x| > c\}.$$ The advantage is that one only needs three definitions for limits (left, right, and central) to cover all the cases. As presented above, for a completely rigorous account, we would need to consider 15 separate cases for each combination of infinities (five directions: −∞, left, central, right, and +∞; three bounds: −∞, finite, or +∞). There are also noteworthy pitfalls. For example, when working with the extended real line, $$x^{-1}$$ does not possess a central limit (which is normal):

$$\lim_{x \to 0^{+}}{1\over x} = +\infty, \quad \lim_{x \to 0^{-}}{1\over x} = -\infty.$$

In contrast, when working with the projective real line, infinities (much like 0) are unsigned, so, the central limit does exist in that context:

$$\lim_{x \to 0^{+}}{1\over x} = \lim_{x \to 0^{-}}{1\over x} = \lim_{x \to 0}{1\over x} = \infty.$$

In fact there are a plethora of conflicting formal systems in use. In certain applications of numerical differentiation and integration, it is, for example, convenient to have signed zeroes. A simple reason has to do with the converse of $$\lim_{x \to 0^{-}}{x^{-1}} = -\infty,$$ namely, it is convenient for $$\lim_{x \to -\infty}{x^{-1}} = -0$$ to be considered true. Such zeroes can be seen as an approximation to infinitesimals.

Limits at infinity for rational functions
There are three basic rules for evaluating limits at infinity for a rational function $$f(x) = \tfrac{p(x)}{q(x)}$$ (where $x$ and $p$ are polynomials):
 * If the degree of $c \in \R,$ is greater than the degree of $c \in \R,$, then the limit is positive or negative infinity depending on the signs of the leading coefficients;
 * If the degree of $a \in \R$ and $\R.$ are equal, the limit is the leading coefficient of $\overline \R$ divided by the leading coefficient of $\R \cup \{-\infty, +\infty\}$;
 * If the degree of $\R \cup \{\infty\}$ is less than the degree of $p$, the limit is 0.

If the limit at infinity exists, it represents a horizontal asymptote at $0 < |x − p| < δ$. Polynomials do not have horizontal asymptotes; such asymptotes may however occur with rational functions.

Ordinary limits
By noting that $x0 = 1$ represents a distance, the definition of a limit can be extended to functions of more than one variable. In the case of a function $$f : S \times T \to \R$$ defined on $$S \times T \subseteq \R^2,$$ we defined the limit as follows: the limit of $q$ as $x = 0$ approaches $x = 0$ is $p$, written

$$ \lim_{(x,y) \to (p, q)} f(x, y) = L $$

if the following condition holds:
 * For every $ε > 0$, there exists a $c > 0$ such that for all $q$ in $p$ and $q$ in $p$, whenever $0 < \sqrt{(x-p)^2 + (y-q)^2} < \delta,$ we have $+x > c$,

or formally: $$(\forall \varepsilon > 0)\, (\exists \delta > 0)\, (\forall x \in S) \, (\forall y \in T)\, (0 < \sqrt{(x-p)^2 + (y-q)^2} < \delta \implies |f(x, y) - L| < \varepsilon)).$$

Here $\sqrt{(x-p)^2 + (y-q)^2}$ is the Euclidean distance between $|f(x) − L| < ε$ and $ε > 0$. (This can in fact be replaced by any norm $c > 0$, and be extended to any number of variables.)

For example, we may say $$ \lim_{(x,y) \to (0, 0)} \frac{x^4}{x^2+y^2} = 0 $$ because for every $x < −c$, we can take $\delta = \sqrt \varepsilon$ such that for all real $|f(x) − L| < ε$ and real $ε > 0$, if $0 < \sqrt{(x-0)^2 + (y-0)^2} < \delta,$  then $c = 3/ε$.

Similar to the case in single variable, the value of $q$ at $x > c$ does not matter in this definition of limit.

For such a multivariable limit to exist, this definition requires the value of $p$ approaches $q$ along every possible path approaching $|f(x) − 4| < ε$. In the above example, the function $$f(x, y) = \frac{x^4}{x^2+y^2}$$ satisfies this condition. This can be seen by considering the polar coordinates $$(x,y) = (r\cos\theta, r\sin\theta) \to (0, 0),$$ which gives $$\lim_{r \to 0} f(r \cos \theta, r \sin \theta) = \lim_{r \to 0} \frac{r^4 \cos^4 \theta}{r^2} = \lim_{r \to 0} r^2 \cos^4 \theta.$$ Here $ε > 0$ is a function of r which controls the shape of the path along which $f$ is approaching $c = max{1, −ln(ε)}$. Since $x < −c$ is bounded between [−1, 1], by the sandwich theorem, this limit tends to 0.

In contrast, the function $$f(x, y) = \frac{xy}{x^2 + y^2}$$ does not have a limit at $|f(x) − 0| < ε$. Taking the path $N > 0$, we obtain $$\lim_{t \to 0} f(t, 0) = \lim_{t \to 0} \frac{0}{t^2} = 0,$$ while taking the path $δ > 0$, we obtain $$\lim_{t \to 0} f(t, t) = \lim_{t \to 0} \frac{t^2}{t^2 + t^2} = \frac{1}{2}.$$

Since the two values do not agree, $L$ does not tend to a single value as $0 < |x − p| < δ$ approaches $f(x) > N$.

Multiple limits
Although less commonly used, there is another type of limit for a multivariable function, known as the multiple limit. For a two-variable function, this is the double limit. Let $$f : S \times T \to \R$$ be defined on $$S \times T \subseteq \R^2,$$ we say the double limit of $x$ as $S$ approaches $y$ and $T$ approaches $f$ is $f$, written

$$ \lim_{ {x \to p} \atop {y \to q} } f(x, y) = L $$

if the following condition holds:

$$(\forall \varepsilon > 0)\, (\exists \delta > 0)\, (\forall x \in S) \, (\forall y \in T)\, ( (0 < |x-p| < \delta) \land (0 < |y-q| < \delta) \implies |f(x, y) - L| < \varepsilon) .$$

For such a double limit to exist, this definition requires the value of $L$ approaches $f$ along every possible path approaching $N > 0$, excluding the two lines $δ > 0$ and $0 < |x − p| < δ$. As a result, the multiple limit is a weaker notion than the ordinary limit: if the ordinary limit exists and equals $f$, then the multiple limit exists and also equals $f$. The converse is not true: the existence of the multiple limits does not imply the existence of the ordinary limit. Consider the example $$f(x,y) = \begin{cases} 1 \quad \text{for} \quad xy \ne 0 \\ 0 \quad \text{for} \quad xy = 0 \end{cases}$$ where $$ \lim_{ {x \to 0} \atop {y \to 0} } f(x, y) = 1 $$ but $$\lim_{(x, y) \to (0, 0)} f(x, y)$$ does not exist.

If the domain of $x$ is restricted to $$(S\setminus\{p\}) \times (T\setminus\{q\}),$$ then the two definitions of limits coincide.

Multiple limits at infinity
The concept of multiple limit can extend to the limit at infinity, in a way similar to that of a single variable function. For $$f : S \times T \to \R,$$ we say the double limit of $p$ as $y$ and $q$ approaches infinity is $L$, written $$ \lim_{ {x \to \infty} \atop {y \to \infty} } f(x, y) = L $$

if the following condition holds:

$$(\forall \varepsilon > 0)\, (\exists c> 0)\, (\forall x \in S) \, (\forall y \in T)\, ( (x > c) \land (y > c) \implies |f(x, y) - L| < \varepsilon) .$$

We say the double limit of $x$ as $S$ and $y$ approaches minus infinity is $T$, written $$ \lim_{ {x \to -\infty} \atop {y \to -\infty} } f(x, y) = L $$

if the following condition holds:

$$(\forall \varepsilon > 0)\, (\exists c> 0)\, (\forall x \in S) \, (\forall y \in T)\, ( (x < -c) \land (y < -c) \implies |f(x, y) - L| < \varepsilon) .$$

Pointwise limits and uniform limits
Let $$f : S \times T \to \R.$$ Instead of taking limit as $f(x) < −N$, we may consider taking the limit of just one variable, say, $N > 0$, to obtain a single-variable function of $f$, namely $$g : T \to \R.$$ In fact, this limiting process can be done in two distinct ways. The first one is called pointwise limit. We say the pointwise limit of $L$ as $L$ approaches $L$ is $f$, denoted $$\lim_{x\to p}f(x, y) = g(y),$$ or $$\lim_{x \to p}f(x, y) = g(y) \;\; \text{pointwise}.$$

Alternatively, we may say $f$ tends to $x$ pointwise as $y$ approaches $L$, denoted $$f(x, y) \to g(y) \;\; \text{as} \;\; x \to p,$$ or $$f(x, y) \to g(y) \;\; \text{pointwise} \;\; \text{as} \;\; x \to p.$$

This limit exists if the following holds:

$$(\forall \varepsilon > 0)\, (\forall y \in T) \, (\exists \delta> 0)\, (\forall x \in S)\, ( 0 < |x-p| < \delta \implies |f(x, y) - g(y)| < \varepsilon) .$$

Here, $x > 0$ is a function of both $x$ and $S$. Each $y$ is chosen for a specific point of $T$. Hence we say the limit is pointwise in $f$. For example, $$f(x, y) = \frac{x}{\cos y}$$ has a pointwise limit of constant zero function $$\lim_{x \to 0}f(x, y) = 0(y) \;\; \text{pointwise}$$ because for every fixed $x$, the limit is clearly 0. This argument fails if $y$ is not fixed: if $L$ is very close to $0 < x − 1 < δ$, the value of the fraction may deviate from 0.

This leads to another definition of limit, namely the uniform limit. We say the uniform limit of $x$ on $S$ as $y$ approaches $T$ is $y$, denoted $$\underset{ {x \to p} \atop {y \in T} }{\mathrm{unif} \lim \;} f(x, y) = g(y),$$ or $$\lim_{x \to p}f(x, y) = g(y) \;\; \text{uniformly on} \; T.$$

Alternatively, we may say $f$ tends to $x$ uniformly on $p$ as $g$ approaches $f$, denoted $$f(x, y) \rightrightarrows g(y) \; \text{on} \; T \;\; \text{as} \;\; x \to p,$$ or $$f(x, y) \to g(y) \;\; \text{uniformly on}\; T \;\; \text{as} \;\; x \to p.$$

This limit exists if the following holds:

$$(\forall \varepsilon > 0) \, (\exists \delta > 0)\, (\forall x \in S)\, (\forall y \in T)\, ( 0 < |x-p| < \delta \implies |f(x, y) - g(y)| < \varepsilon) .$$

Here, $f(x) > N$ is a function of only $g$ but not $x$. In other words, δ is uniformly applicable to all $p$ in $y$. Hence we say the limit is uniform in $T$. For example, $$f(x, y) = x \cos y$$ has a uniform limit of constant zero function $$\lim_{x \to 0}f(x, y) = 0(y) \;\; \text{ uniformly on}\; \R$$ because for all real $x$, $N > 0$ is bounded between $δ = e^{−N}$. Hence no matter how $S$ behaves, we may use the sandwich theorem to show that the limit is 0.

Iterated limits
Let $$f : S \times T \to \R.$$ We may consider taking the limit of just one variable, say, $x > 0$, to obtain a single-variable function of $ε$, namely $$g : T \to \R,$$ and then take limit in the other variable, namely $0 < x − 0 < δ$, to get a number $y$. Symbolically, $$\lim_{y \to q} \lim_{x \to p} f(x, y) = \lim_{y \to q} g(y) = L.$$

This limit is known as iterated limit of the multivariable function. The order of taking limits may affect the result, i.e.,

$$\lim_{y \to q} \lim_{x \to p} f(x,y) \ne \lim_{x \to p} \lim_{y \to q} f(x, y)$$ in general.

A sufficient condition of equality is given by the Moore-Osgood theorem, which requires the limit $$\lim_{x \to p}f(x, y) = g(y)$$ to be uniform on $δ$.

Functions on metric spaces
Suppose $y$ and $y$ are subsets of metric spaces $y$ and $y$, respectively, and $f(x) < −N$ is defined between $y$ and $f$, with $[−∞, c)$, $T$ a limit point of $x$ and $(c, ∞]$. It is said that the limit of $p$ as $g$ approaches $f$ is $g$ and write

$$ \lim_{x \to p}f(x) = L $$

if the following property holds:

$$(\forall \varepsilon > 0 )\, (\exists \delta > 0) \,(\forall x \in M) \,(0 < d_A(x, p) < \delta \implies d_B(f(x), L) < \varepsilon).$$

Again, note that $T$ need not be in the domain of $x$, nor does $p$ need to be in the range of $x$, and even if $y = 4$ is defined it need not be equal to $S$.

Euclidean metric
The limit in Euclidean space is a direct generalization of limits to vector-valued functions. For example, we may consider a function $$f:S \times T \to \R^3$$ such that $$f(x, y) = (f_1(x, y), f_2(x, y), f_3(x, y) ).$$ Then, under the usual Euclidean metric, $$\lim_{(x, y) \to (p, q)} f(x, y) = (L_1, L_2, L_3)$$ if the following holds:

$$(\forall \varepsilon > 0 )\, (\exists \delta > 0) \, (\forall x \in S) \, (\forall y \in T)\, \left(0 < \sqrt{(x-p)^2+(y-q)^2} < \delta \implies \sqrt{(f_1-L_1)^2 + (f_2-L_2)^2 + (f_3-L_3)^2} < \varepsilon \right).$$

In this example, the function concerned are finite-dimension vector-valued function. In this case, the limit theorem for vector-valued function states that if the limit of each component exists, then the limit of a vector-valued function equals the vector with each component taken the limit: $$\lim_{(x, y) \to (p, q)} \Bigl(f_1(x, y), f_2(x, y), f_3(x, y)\Bigr) = \left(\lim_{(x, y) \to (p, q)}f_1(x, y), \lim_{(x, y) \to (p, q)}f_2(x, y), \lim_{(x, y) \to (p, q)}f_3(x, y)\right).$$

Manhattan metric
One might also want to consider spaces other than Euclidean space. An example would be the Manhattan space. Consider $$f:S \to \R^2$$ such that $$f(x) = (f_1(x), f_2(x)).$$ Then, under the Manhattan metric, $$\lim_{x \to p} f(x) = (L_1, L_2)$$ if the following holds:

$$(\forall \varepsilon > 0 )\, (\exists \delta > 0) \,(\forall x \in S) \,(0 < |x - p| < \delta \implies |f_1 - L_1| + |f_2 - L_2| < \varepsilon).$$

Since this is also a finite-dimension vector-valued function, the limit theorem stated above also applies.

Uniform metric
Finally, we will discuss the limit in function space, which has infinite dimensions. Consider a function $y = L$ in the function space $$S \times T \to \R.$$ We want to find out as $y$ approaches $T$, how $|x − p|$ will tend to another function $(x, y)$, which is in the function space $$T \to \R.$$ The "closeness" in this function space may be measured under the uniform metric. Then, we will say the uniform limit of $ε$ on $y$ as $y$ approaches $T$ is $y$ and write $$\underset{ {x \to p} \atop {y \in T} }{\mathrm{unif} \lim \;} f(x, y) = g(y),$$ or $$\lim_{x \to p}f(x, y) = g(y) \;\; \text{uniformly on} \; T,$$

if the following holds:

$$(\forall \varepsilon > 0 )\, (\exists \delta > 0) \,(\forall x \in S) \,(0 < |x-p| < \delta \implies \sup_{y \in T} | f(x, y) - g(y) | < \varepsilon).$$

In fact, one can see that this definition is equivalent to that of the uniform limit of a multivariable function introduced in the previous section.

Functions on topological spaces
Suppose $y$ and $y$ are topological spaces with $y$ a Hausdorff space. Let $L$ be a limit point of $(p, q)$, and $ε > 0$. For a function $δ > 0$, it is said that the limit of $T$ as $M$ approaches $N$ is $A$, written

$$ \lim_{x \to p}f(x) = L ,$$

if the following property holds:

This last part of the definition can also be phrased "there exists an open punctured neighbourhood $B$ of $M$ such that $|f(x, y) − L| < ε$".

The domain of $N$ does not need to contain $p$. If it does, then the value of $M$ at $f$ is irrelevant to the definition of the limit. In particular, if the domain of $x$ is $(x, y)$ (or all of $p$), then the limit of $L$ as $(p, q)$ exists and is equal to $p$ if, for all subsets $||(x, y) − (p, q)||$ of $f$ with limit point $L$, the limit of the restriction of $f$ to $ε > 0$ exists and is equal to $L$. Sometimes this criterion is used to establish the non-existence of the two-sided limit of a function on $x$ by showing that the one-sided limits either fail to exist or do not agree. Such a view is fundamental in the field of general topology, where limits and continuity at a point are defined in terms of special families of subsets, called filters, or generalized sequences known as nets.

Alternatively, the requirement that $S$ be a Hausdorff space can be relaxed to the assumption that $y$ be a general topological space, but then the limit of a function may not be unique. In particular, one can no longer talk about the limit of a function at a point, but rather a limit or the set of limits at a point.

A function is continuous at a limit point $T$ of and in its domain if and only if $x ≠ 0$ is the (or, in the general case, a) limit of $y ≠ 0$ as $x$ tends to $S$.

There is another type of limit of a function, namely the sequential limit. Let $|f(x, y) − 0| < ε$ be a mapping from a topological space $x$ into a Hausdorff space $p$, $(p, q)$ a limit point of $f$ and $(p, q)$. The sequential limit of $T$ as $x$ tends to $p$ is $g$ if

 * For every sequence ($x$) in $θ = θ(r)$ that converges to $S$, the sequence $(p, q)$ converges to $X$.

If $Y$ is the limit (in the sense above) of $Y$ as $p$ approaches $f$, then it is a sequential limit as well, however the converse need not hold in general. If in addition $x$ is metrizable, then $p$ is the sequential limit of $L$ as $V$ approaches $L$ if and only if it is the limit (in the sense above) of $U$ as $p$ approaches $U$.

In terms of sequences
For functions on the real line, one way to define the limit of a function is in terms of the limit of sequences. (This definition is usually attributed to Eduard Heine.) In this setting: $$\lim_{x\to a}f(x)=L$$ if, and only if, for all sequences $p$ (with $f$ not equal to $p$ for all $f$) converging to $p$ the sequence $cos θ$ converges to $f$. It was shown by Sierpiński in 1916 that proving the equivalence of this definition and the definition above, requires and is equivalent to a weak form of the axiom of choice. Note that defining what it means for a sequence $X$ to converge to $f$ requires the epsilon, delta method.

Similarly as it was the case of Weierstrass's definition, a more general Heine definition applies to functions defined on subsets of the real line. Let $L$ be a real-valued function with the domain $(0, 0)$. Let $X$ be the limit of a sequence of elements of $(x, y) = (t, 0) → (0, 0)$ Then the limit (in this sense) of $p$ is $f$ as $L$ approaches $\R$ if for every sequence $(x, y) = (t, t) → (0, 0)$ (so that for all $Y$, $Y$ is not equal to $p$) that converges to $x$, the sequence $(x, y)$ converges to $p$. This is the same as the definition of a sequential limit in the preceding section obtained by regarding the subset $(0, 0)$ of $X$ as a metric space with the induced metric.

In non-standard calculus
In non-standard calculus the limit of a function is defined by: $$\lim_{x\to a}f(x)=L$$ if and only if for all $$x\in \R^*,$$ $$f^*(x)-L$$ is infinitesimal whenever $ε > 0$ is infinitesimal. Here $$\R^*$$ are the hyperreal numbers and $Y$ is the natural extension of $X$ to the non-standard real numbers. Keisler proved that such a hyperreal definition of limit reduces the quantifier complexity by two quantifiers. On the other hand, Hrbacek writes that for the definitions to be valid for all hyperreal numbers they must implicitly be grounded in the ε-δ method, and claims that, from the pedagogical point of view, the hope that non-standard calculus could be done without ε-δ methods cannot be realized in full. Bŀaszczyk et al. detail the usefulness of microcontinuity in developing a transparent definition of uniform continuity, and characterize Hrbacek's criticism as a "dubious lament".

In terms of nearness
At the 1908 international congress of mathematics F. Riesz introduced an alternate way defining limits and continuity in concept called "nearness". A point $f$ is defined to be near a set $$A\subseteq \R$$ if for every $δ > 0$ there is a point $0 < |x − p| < δ$ so that $0 < |y − q| < δ$. In this setting the $$\lim_{x\to a} f(x)=L$$ if and only if for all $$A\subseteq \R,$$ $x$ is near $|f(x, y) − L| < ε$ whenever $p$ is near $L$. Here $(p, q)$ is the set $$\{f(x) | x \in A\}.$$ This definition can also be extended to metric and topological spaces.

Relationship to continuity
The notion of the limit of a function is very closely related to the concept of continuity. A function $x_{n}$ is said to be continuous at $p$ if it is both defined at $L$ and its value at $L$ equals the limit of $f$ as $x$ approaches $p$:

$$\lim_{x\to c} f(x) = f(c).$$ We have here assumed that $X$ is a limit point of the domain of $L$.

Properties
If a function $f$ is real-valued, then the limit of $x$ at $p$ is $f$ if and only if both the right-handed limit and left-handed limit of $x$ at $p$ exist and are equal to $xn$.

The function $xn$ is continuous at $a$ if and only if the limit of $x = p$ as $n$ approaches $a$ exists and is equal to $y = q$. If $ε > 0$ is a function between metric spaces $L$ and $xn$, then it is equivalent that $a$ transforms every sequence in $f$ which converges towards $a$ into a sequence in $f$ which converges towards $c > 0$.

If $L$ is a normed vector space, then the limit operation is linear in the following sense: if the limit of $x > c$ as $x$ approaches $p$ is $n$ and the limit of $y > c$ as $xn$ approaches $a$ is $a$, then the limit of $|f(x, y) − L| < ε$ as $L$ approaches $\R$ is $ε > 0$. If $f*$ is a scalar from the base field, then the limit of $c > 0$ as $f$ approaches $x$ is $L$.

If $a$ and $A$ are real-valued (or complex-valued) functions, then taking the limit of an operation on $x < −c$ and $y < −c$ (e.g., $|f(x, y) − L| < ε$, $(x, y) → (p, q)$, $x → p$, $ε > 0$, $f$) under certain conditions is compatible with the operation of limits of $δ(ε, y) > 0$ and $0 < |x − p| < δ$. This fact is often called the algebraic limit theorem. The main condition needed to apply the following rules is that the limits on the right-hand sides of the equations exist (in other words, these limits are finite values including 0). Additionally, the identity for division requires that the denominator on the right-hand side is non-zero (division by 0 is not defined), and the identity for exponentiation requires that the base is positive, or zero while the exponent is positive (finite).

$$\begin{array}{lcl} \displaystyle \lim_{x \to p} (f(x) + g(x)) & = & \displaystyle \lim_{x \to p} f(x) + \lim_{x \to p} g(x) \\ \displaystyle \lim_{x \to p} (f(x) - g(x)) & = & \displaystyle \lim_{x \to p} f(x) - \lim_{x \to p} g(x) \\ \displaystyle \lim_{x \to p} (f(x)\cdot g(x)) & = & \displaystyle \lim_{x \to p} f(x) \cdot \lim_{x \to p} g(x) \\ \displaystyle \lim_{x \to p} (f(x)/g(x)) & = & \displaystyle {\lim_{x \to p} f(x) / \lim_{x \to p} g(x)} \\ \displaystyle \lim_{x \to p} f(x)^{g(x)} & = & \displaystyle {\lim_{x \to p} f(x) ^ {\lim_{x \to p} g(x)}} \end{array}$$

These rules are also valid for one-sided limits, including when $c$ is ∞ or −∞. In each rule above, when one of the limits on the right is ∞ or −∞, the limit on the left may sometimes still be determined by the following rules.

$$\begin{array}{rcl} q + \infty & = & \infty \text{ if } q \neq -\infty \\[8pt] q \times \infty & = & \begin{cases} \infty & \text{if } q > 0 \\ -\infty & \text{if } q < 0 \end{cases} \\[6pt] \displaystyle \frac q \infty & = & 0 \text{ if } q \neq \infty \text{ and } q \neq -\infty \\[6pt] \infty^q & = & \begin{cases} 0 & \text{if } q < 0 \\ \infty & \text{if } q > 0 \end{cases} \\[4pt] q^\infty & = & \begin{cases} 0 & \text{if } 0 < q < 1 \\ \infty & \text{if } q > 1 \end{cases} \\[4pt] q^{-\infty} & = & \begin{cases} \infty & \text{if } 0 < q < 1 \\ 0 & \text{if } q > 1 \end{cases} \end{array}$$

(see also Extended real number line).

In other cases the limit on the left may still exist, although the right-hand side, called an indeterminate form, does not allow one to determine the result. This depends on the functions $c$ and $c$. These indeterminate forms are:

$$\begin{array}{cc} \displaystyle \frac{0}{0} & \displaystyle \frac{\pm \infty}{\pm \infty} \\[6pt] 0 \times \pm \infty & \infty + -\infty \\[8pt] \qquad 0^0 \qquad & \qquad \infty^0 \qquad \\[8pt] 1^{\pm \infty} \end{array}$$

See further L'Hôpital's rule below and Indeterminate form.

Limits of compositions of functions
In general, from knowing that $$\lim_{y \to b} f(y) = c$$ and $$\lim_{x \to a} g(x) = b,$$ it does not follow that $$\lim_{x \to a} f(g(x)) = c.$$ However, this "chain rule" does hold if one of the following additional conditions holds:
 * $|f(x, y) − g(y)| < ε$ (that is, $f$ is continuous at $x$), or
 * $c$ does not take the value $c$ near  $f$ (that is, there exists a $δ = δ(ε, y)$ such that if $π/2$ then $ε > 0$).

As an example of this phenomenon, consider the following function that violates both additional restrictions:

$$f(x) = g(x) = \begin{cases} 0 & \text{if } x\neq 0 \\ 1 & \text{if } x=0 \end{cases}$$

Since the value at $δ(ε) > 0$ is a removable discontinuity, $$\lim_{x \to a} f(x) = 0$$ for all $f$. Thus, the naïve chain rule would suggest that the limit of $0 < |x − p| < δ$ is 0. However, it is the case that $$f(f(x))=\begin{cases} 1 & \text{if } x\neq 0 \\ 0 & \text{if } x = 0 \end{cases}$$ and so $$\lim_{x \to a} f(f(x)) = 1$$ for all $f$.

Rational functions
For $p$ a nonnegative integer and constants $$a_1, a_2, a_3,\ldots, a_n$$ and $$b_1, b_2, b_3,\ldots, b_n,$$

$$\lim_{x \to \infty} \frac{a_1 x^n + a_2 x^{n-1} + a_3 x^{n-2} + \dots + a_n}{b_1 x^n + b_2 x^{n-1} + b_3 x^{n-2} + \dots + b_n} = \frac{a_1}{b_1}$$

This can be proven by dividing both the numerator and denominator by $L$. If the numerator is a polynomial of higher degree, the limit does not exist. If the denominator is of higher degree, the limit is 0.

Trigonometric functions
$$\begin{array}{lcl} \displaystyle \lim_{x \to 0} \frac{\sin x}{x} & = & 1 \\[4pt] \displaystyle \lim_{x \to 0} \frac{1 - \cos x}{x} & = & 0 \end{array}$$

Exponential functions
$$\begin{array}{lcl} \displaystyle \lim_{x \to 0} (1+x)^{\frac{1}{x}} & = & \displaystyle \lim_{r \to \infty} \left(1+\frac{1}{r}\right)^r = e \\[4pt] \displaystyle \lim_{x \to 0} \frac{e^{x}-1}{x} & = & 1 \\[4pt] \displaystyle \lim_{x \to 0} \frac{e^{ax}-1}{bx} & = & \displaystyle \frac{a}{b} \\[4pt] \displaystyle \lim_{x \to 0} \frac{c^{ax}-1}{bx} & = & \displaystyle \frac{a}{b}\ln c \\[4pt] \displaystyle \lim_{x \to 0^+} x^x & = & 1 \end{array}$$

Logarithmic functions
$$\begin{array}{lcl} \displaystyle \lim_{x \to 0} \frac{\ln(1+x)}{x} & = & 1 \\[4pt] \displaystyle \lim_{x \to 0} \frac{\ln(1+ax)}{bx} & = & \displaystyle \frac{a}{b} \\[4pt] \displaystyle \lim_{x \to 0} \frac{\log_c(1+ax)}{bx} & = & \displaystyle \frac{a}{b\ln c} \end{array}$$

L'Hôpital's rule
This rule uses derivatives to find limits of indeterminate forms $|f(x, y) − g(y)| < ε$ or $δ = δ(ε)$, and only applies to such cases. Other indeterminate forms may be manipulated into this form. Given two functions $cos y$ and $[−1, 1]$, defined over an open interval $f$ containing the desired limit point $p$, then if: then: $$\lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)}.$$
 * 1) $$\lim_{x \to c}f(x)=\lim_{x \to c}g(x)=0,$$  or $$\lim_{x \to c}f(x)=\pm\lim_{x \to c}g(x) = \pm\infty,$$ and
 * 2) $$f$$ and $$g$$ are differentiable over $$I \setminus \{c\},$$ and
 * 3) $$g'(x)\neq 0$$ for all $$ x \in I \setminus \{c\},$$ and
 * 4) $$\lim_{x\to c}\tfrac{f'(x)}{g'(x)}$$  exists,

Normally, the first condition is the most important one.

For example: $$\lim_{x \to 0} \frac{\sin (2x)}{\sin (3x)} = \lim_{x \to 0} \frac{2 \cos (2x)}{3 \cos (3x)} = \frac{2 \sdot 1}{3 \sdot 1} = \frac{2}{3}.$$

Summations and integrals
Specifying an infinite bound on a summation or integral is a common shorthand for specifying a limit.

A short way to write the limit $$\lim_{n \to \infty} \sum_{i=s}^n f(i) $$ is $$\sum_{i=s}^\infty f(i).$$ An important example of limits of sums such as these are series.

A short way to write the limit $$\lim_{x \to \infty} \int_a^x f(t) \; dt $$ is $$\int_a^\infty f(t) \; dt.$$

A short way to write the limit $$\lim_{x \to -\infty} \int_x^b f(t) \; dt $$ is $$\int_{-\infty}^b f(t) \; dt.$$

title: Limit of a function


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Mary Poppins
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nice work
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ArbCom elections are now open!
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title: User talk:Dr jkl


text:
User talk:Braininfo.rprc.washington.edu

Hello there, welcome to the 'pedia! I hope you like the place and decide to stay. If you need pointers on how we title pages visit Naming conventions or how to format them visit our manual of style. If you have any other questions about the project then check out Help or add a question to the Village pump. Cheers! --maveric149

Basal ganglia
Hi -- are you aware that the link you added to the article is already present in the "infobox" at the top, under the label "NeuroNames"? Looie496 (talk) 23:18, 1 June 2011 (UTC)
 * Please respond to this message. Looie496 (talk) 17:03, 6 June 2011 (UTC)

Test reply. We are in receipt of your message and will respond shortly. Braininfo.rprc.washington.edu (talk) 15:28, 9 June 2011 (UTC)

 * Okay, I'll wait. Looie496 (talk) 21:32, 9 June 2011 (UTC)

Dear Mr. Looie496,

Thanks for your message. I had heard that the Society for Neuroscience was encouraging members to help populate Wikipedia with neurosci information and wanted to correspond with someone about it.

We tried to link from Wikipedia to appropriate pages of BrainInfo (then called 'NeuroNames') many years ago, but our links were scrubbed after a few days, because they were judged by someone at Wikipedia to be advertising. We've always thought that was unjust, because BrainInfo is an academic website developed specifically to provide scientific information about central nervous system structures to scientists, students and the general public. Later someone else created the NeuroNames links that you referred to in your message, and we've been pleased to see them there.

Yes, we're aware of the NeuroNames links, but don't believe that they are as valuable to users as they might be. They link through an old template URL, so many of the structures added to BrainInfo in the last couple of years are not accessible. Also, the tag NeuroNames, which refers to the ontology of the BrainInfo website, suggests that by clicking there the user will learn more about the many names for the structure. In fact they will, but they will have to navigate to the names page after they get to BrainInfo. We'd like to go through Wikipedia and change the NeuroNames links so that they bring up the names table, which contains all of the names in English, Latin and six other languages. For example see the several legitimate English and Latin names for field H at: http://braininfo.rprc.washington.edu/synonyms.aspx?questID=440

The entry that caught your attention reflected something we'd like to do at the same time, namely insert into Wikipedia's External Links section a link to BrainInfo's Central Directory for each structure. The hyperlink would be preceded by a couple of words to indicate the broader range of information the visitor will find there... something like 'More info at [link]' For example see the description, internal structure and illustration of area 46 of Walker at: http://braininfo.rprc.washington.edu/centraldirectory.aspx?ID=962

During the last couple of weeks we went through the BrainInfo site and installed some 500 links to Wikipedia pages that have information on the function and/or medical significance of structures. If you have no objections, we'll continue that for as many of the other 1700 NeuroNames structures as Wikipedia has functional and medical information for. See for example Wikipedia's page for 'striatum' by navigating thru: http://braininfo.rprc.washington.edu/centraldirectory.aspx?ID=225 and click 'Functions and Medical Importance'.

So, what is your thinking on all this... particularly the idea of including both a link to NeuroNames for synonyms and to BrainInfo for other kinds of information that may not be in Wikipedia yet?

With best regards,

Doug Bowden http://braininfo.org dmbowden@uw.edu Braininfo.rprc.washington.edu (talk) 00:03, 10 June 2011 (UTC)

 * Thanks for explaining. That all makes sense, but I wonder if a better solution might not be to fix the infobox.  If you would like to have NeuroNames changed to BrainInfo, I can do that in the infobox template, and all of the articles that use it will change instantly.  In that case all you will have to do is change the link in the infobox in each article.  Or if you would like both things to be present in the infobox, that would also be possible, although it gets dangerously close to clutter.  The most important thing in any case is that there be some sort of agreement on the approach before you plunge into mass editing.

 * There is another issue that I probably should alert you to. Wikipedia policy is that editors are individual people, not official representatives of organizations, and should not choose user-names that indicate any sort of official status.  If you do mass editing, you are likely to get flak about this, and sooner or later (possibly very soon) you will be required to change your user name.  Regards, and thanks for the information. Looie496 (talk) 16:35, 11 June 2011 (UTC)

I agree with all of the above... let's get the policy issue resolved first. The last thing I want to do is get bounced again.

Just for point of clarification: Who is the 'editor' in this case... you or I? If I, can I change my user name? or is it better to delete the 'Braininfo.rprc.washington.edu' account and create a new account?

Is there any reason I shouldn't use my real name, e.g., dmbowden?

I like the idea of having the links to NeuroNames/BrainInfo in the infobox, but think it would be more useful to have the labels be, not 'NeuroNames' and/or 'BrainInfo', but words that are more informative to the user regarding what kind of information he'll get if he clicks there, e.g., 'Other Names', or 'Synonyms' (for the link to NeuroNames); 'More Information' or 'More Info' (for a link to BrainInfo's central directory for the structure). Is that possible in the infobox, or does it have to be the name of the website?

I'd prefer to have both buttons there, but if you think the box is getting too cluttered, I'd honor your judgment and just put up the button that links to BrainInfo's central directory. Maybe if there are not more than n entries in the infobox we'd enter both; if >n we'd enter only the 'More Info' link to the central directory... and you tell us an appropriate value of n.

One last question: before Saving a page like this, should I click one or the other of the boxes for 'minor edit' or 'Watch this page'?

Many Thanks, Doug B

 * You have so few edits that going through the process of changing your account name is probably not worth the effort -- creating a new one is simpler. If you do, that, though, please leave a message at User talk:Looie496 so I can find you.  The only reason not to use your real name would be a concern about controversies on Wikipedia carrying over to the outside world -- that's my reason, but it probably doesn't apply to you.  Regarding the infobox, I think what you are describing is possible, but I didn't understand it very clearly.  Regards, Looie496 (talk) 00:16, 17 June 2011 (UTC)

title: User talk:Braininfo.rprc.washington.edu


text:
User talk:Dan anderson

Hello there, welcome to the 'pedia! I hope you like the place and decide to stay. If you need pointers on how we title pages visit Naming conventions or how to format them visit our manual of style. If you have any other questions about the project then check out Help or add a question to the Village pump. Cheers! --maveric149

discuss philosophy
hi, I need some advice from some profesional philosopher and u are one, so I was wondering if u could have some time to talk to me. thanx. --Cosmic girl 17:51, 14 January 2006 (UTC)

Speedy deletion of Australian National University
You can ignore this, someone had replaced the page with patent nonsense. It's now been reverted, not deleted. I initially hit the wrong key in twinkle and accidentally tagged instead of reverted. Cheers, -- B figura (talk) 00:51, 1 October 2007 (UTC)

title: User talk:Dan anderson


text:
Talk:N. Chandrababu Naidu

Mass revert
@Chinnusaikrish Why did you revert my edits as well as that of the other editor? I did not remove any incidents or present anything in a substantively different way. Those were simple incremental edits meant to improve structure. Very very little was removed by myself, such as the word "miserably" which is unencyclopedic WP:TONE. Please restore all those edits of mine which you don't actually object to, and we will discuss those that you do object to. Regards —Alalch E. 18:33, 24 December 2022 (UTC)

@ChinnusaikrishThe tone that you added is clearly disruptive and is not according to the concensus. Most of the sources you cited belong to unreliable websites- not secured as per Wikipedia. There's clearly no point of neutrality. Other sources are mere political statements by people from other parties as part of political allegations cannot be taken as souces. There must be strong evidence of secondary sources. 4 5 6 legend (talk) 18:36, 24 December 2022 (UTC)

hello @User:Alalch E., I reverted his edits as of now again. We will wait from hom to discuss. 4 5 6 legend (talk) 18:37, 24 December 2022 (UTC)

 * By WP:BOLDly proceeding with your idea about what should be removed, I now understand what you talked about, with regard to describing actions of entities who are not exactly Naidu individually. However, I don't agree with you that this should be removed. It's relevant because he was the party leader. I prefer that the removed content be restored first, but we can still discuss it. —Alalch E. 19:36, 24 December 2022 (UTC)

 * Alalch E., Yes we must discuss before performing any actions, but to explain further the user already disrupted multiple pages with a negative tone and also has been warned by another user. He already is having a biased nature of editing (refer to his edit history, that I have observed today of his past edits), In this case I don't think we need to restore the content this user added. Or are you referring to the previous content that this user removed? 4 5 6 legend (talk) 19:50, 24 December 2022 (UTC)

 * Also to mention as you said you can mention about other enties but is it really required to glorify the foreign entities that do not belong to this subject. I also don't mean that we need to glorify this subject. I just wanted to say that we must ensure neutrality. The words like complete, entire, overall is subject to question of the neutrality. This page was already effected with a fan point of view template earlier but that also dosent mean we need to defame the subject in a way so that we can remove the template, that is what exactly this user did here. Lastly I want to say that we need to discuss the facts before restoring the content that this user added because it is very much questionable in the initial instance itself since he added titles with a negative tone, not one or two but all of them...I suppose you were the one who rectified it, so we must discuss before restoring these kind of edits. And to mention this user removed/replaced the sourced content of this subject (check the edit history) does that not say these are clearly disruptive edits? (Still pending to be added them too....are we actually not supposed to restore that part first?) Alaach E. 4 5 6 legend (talk) 19:57, 24 December 2022 (UTC)
 * [ec] I'm talking about these removals diff, which you made. I don't agree with most of them. Most of that content is relevant in this article but the language needs to be more neutral. We do not need to discuss everything before performing actions. /this is a reply to your first comment, as you made two; I can't reply in more detail now/ —Alalch E. 20:02, 24 December 2022 (UTC)

 * The words like "complete useless" is not something neutral. Padayatra of a opponent should be clearly placed on the respective page or okay it's fine to discuss about it. And lastly to the third one was not sources that said "given advantage" and "sympathy" (not sourced) 4 5 6 legend (talk) 20:14, 24 December 2022 (UTC)

 * You are correct that attributing to Naidu a statement that power subsidies to farmers are "completely useless" is unacceptable, based on current sourcing; these words are not in the cited source, and using them to describe his position is not neutral. However, he did oppose the power subsidies; his government raised electricity prices -- that is in the source. So that needs to be said. While Naidu raised prices, the opposition promised free power; this influenced voters, which was a factor in his electoral loss. The source explains this. If we include this information, we are not taking a side; maybe Naidu was right to raise the prices, while the promise of free power by the opposition was a hollow one -- it doesn't matter when we are describing a concrete election cycle. I know that you understand that this is how politics works :) About Reddy's padayatra -- ths is very relevant in the article. It's information necessary to understand how Naidu fell from power. Context is important. This is also in the source. This is an example representing other content which you object to, that needs to be rewritten, not removed. However, regarding this sentence: Chandrababu Naidu who had just escaped from an assination attempt thought of having an advantage of sympathy. -- I completely agree with your removal. That is an example of the prohibited practice of original synthesis. —Alalch E. 17:50, 25 December 2022 (UTC)

 * Yes, I understood, this is what we must do and reach to concensus before adding it. That is what I have suggested the other user to discuss it first. Thank you for understanding the intention. And to mention please see this revision history where the content was blanked without even providing any summary by the same user and he has not yet provided the reason for it. [] 4 5 6 legend (talk) 18:22, 25 December 2022 (UTC)

February 2023
Your major rewrite of the whole article, while probably good in various parts seems to have removed all criticism of Naidu which is against WP:NPOV; please remake this change in a series of incremental edits (section by section) so it's easier to review; some references were removed too such as https://www.thehindu.com/news/national/andhra-pradesh/chandrababu-naidus-son-nara-lokesh-takes-oath-as-minister/article17762250.ece Sincerely. —Alalch E. 12:59, 5 February 2023 (UTC)

 * @Alalch E., I am still in the process of segregation of the content and I will add them accordingly. Since majority of the content was previously removed unexplained. 4 5 6 legend (talk) 13:05, 5 February 2023 (UTC)
 * @Alalch E.You should revert it again by checking the previous edits and add the criticism by yourself instead of removing the sourced content that was previously removed (mass removal) by another user. Please check the edit history. 4 5 6 legend (talk) 13:06, 5 February 2023 (UTC)
 * @Alalch E. sir, I have now added the criticism part too, I think this is enough or are we left with anything else? 4 5 6 legend (talk) 13:35, 5 February 2023 (UTC)

Hello @Alalch E., I have added the criticism part again as a separate section since the previous editor removed the other content. I am still in the process of correcting the data after the analysis of the sources since most of the sources were not claiming any statements. 4 5 6 legend (talk) 13:24, 5 February 2023 (UTC)

 * @Alalch E.I have now added the criticism part in a different section. 4 5 6 legend (talk) 13:36, 5 February 2023 (UTC)
 * I will need to take a closer look. A "criticism section" is something that should be avoided whenever it can. You restored certain points of criticism that you had removed but grouped them all under the criticism heading. That is usually seen as a step back. —Alalch E. 16:55, 5 February 2023 (UTC)

I grouped them because the information was not consistent with any of the categories present. None of the sources actually put forward those particular statements that is present in criticism, but just give a cite about the info. But I ensured to not delete the consistent information for example: the defeat in the 2009 and the backlash from farmers, the criticism of the Opposition and also the cash for vote scam. I haven't removed any of them because it was consistent with the information and was very much neutral like any other wiki article. Anyways you are free to add any further criticism if necessary citations are available and also you are allowed to de-integrate the grouped criticism and add it in the other categories if you feel they are consistent. Other than this, the rest of the info that I have added is sourced content that has been removed unexplained 1 month ago. I hope you analysize the edit history and the article and reach me out for any discussion or concensus if required. 4 5 6 legend (talk) 17:49, 5 February 2023 (UTC)

Untitled
Page is full of misleads and previous pages are removed — Preceding unsigned comment added by Singhal.sasthry (talk • contribs) 06:01, 18 December 2022 (UTC)

Role in National Politics
Chandrababu Naidu's involvement in national politics during an era dominated by non-Congress coalition politics in Delhi is notable. In the aftermath of the 1996 parliamentary elections, he assumed the role of convenor for the United Front, a coalition comprising 13 political parties that secured power at the Centre. The coalition government was headed by H.D. Deve Gowda and later I.K. Gujral between 1996 and 1998. The United Front had its headquarters at Andhra Pradesh Bhavan in New Delhi.

Subsequently, Chandrababu Naidu's significance in national affairs amplified after the 1999 Lok Sabha elections.The TDP and the BJP, which had a pre-poll understanding in the state, together won 36 MPs out of 42. The BJP emerged as the largest single party in the Lok Sabha. The TDP extended the support of 29 of its MPs to the National Democratic Alliance government headed by A.B.Vajpayee. TDP did not join the government, extending only ‘issue-based support’. Naidu claimed that though Vajpayee offered eight cabinet berths to his party, the TDP stayed away from the union cabinet and offered external support. Salivahana (talk) 16:44, 18 July 2023 (UTC)

Lead of the page
Alalch E. Seems u mistook and didn't clearly follow my explanation. I don't intend to present anything in a negative tone but rather in the present status and position of a politician. A politician's recent major electoral achievement or debacle has to be established which were present in my edits. This has nothing to do with the violation of the policy as a politician holds a position in the governmental/public activity. So that has to be represented for a clear understanding of his present status which I did. The lead section added by you has no citations and many of it are way out of context.

Some of it follows: He directed the founding of HITEC city which is false as that was inaugurated and directed by former CM Janardhan Reddy. You even added a sentence about directing the construction of new capital city which is not yet completed or in the mid-way and the matter is sub-judice in the court. These are not needed since they had already been present in the page's respective sections. Mine looks crisp and up to the point. ~ Chinnusaikrish (talk) 07:06, 16 February 2024 (UTC)

 * Mention of HITEC City in the lead follows what is said about it in the body. Things that are present in the body are precisely needed in the lead, because the whole purpose of the lead is to restate them in a summarized way, per MOS:LEAD. A lead section does not need citations per MOS:LEADCITE, unless there is some exceptional reason why a citation would be beneficial. Your "crisp and up to the point" lead is utterly unacceptable. Your "explanation" is terrible and you must urgently give up on this WP:RECENTIST and WP:POV idea, or it may be concluded that you are unable to contribute constructively to this article. —Alalch E. 07:18, 16 February 2024 (UTC)
 * But this way of summarizing whole of the body into the lead didn't quite present a crisp idea and makes it a mini-version of the history of a politician. Is it alright ? And what about the HITEC city issue which was wrongly mentioned and the capital city thing which is sub-judice. These can be included in the respective sections as well. ~ Chinnusaikrish (talk) 07:30, 16 February 2024 (UTC)
 * That's right, it's a mini version of the biography, a summary of the whole biography. See other well-developed articles about politicians, such as Liz Truss or Bill Clinton. Please give me some time to think about mentioning the HITEC City and the other city in the lead. I think that these are due mentions, especially the HITEC City, which is one of the things Naidu is known for, especially in the west (example), but I'm less certain about the need to mention the new capital of AP. —Alalch E. 07:44, 16 February 2024 (UTC)
 * I'm okay with mentioning some of the body here. Mentioning the start of his political journey and some events afterwards are a bit needed. But the whole body of the page is presented as a fan POV where it missed true sense. Summarizing this fan POV body in the lead might not appeal proper as they need more precise explanations which is why I excluded them all. This is where you misunderstood me. And for HITEC City and the capital can be discussed in the respective sections as they seem controversial. ~ Chinnusaikrish (talk) 07:50, 16 February 2024 (UTC)
 * It isn't the same whether HITEC City is controversial as something that may be assessed positively or negatively, or if it's controversial in the sense that sources disagree about whose idea it was and under whose government it was built. There is no controversy in the sources that Naidu is the initiator of the HITEC City project. The same holds for Amaravati. Amaravati seems less important so I've removed it from the time being, but there is not way that removing HITEC City, which is basically the main thing Naidu is known for in the West is appropriate. I agree that the body is pretty weak, and needs much work. As the body of the article is improved, the lead will be adjusted accordingly. —Alalch E. 08:01, 16 February 2024 (UTC)
 * Thanks for making a change and I would like to edit the body as well as many events are not unfolded properly and needed clear explanations with sense which might make the lead more convincing and neutral. And regarding the HITEC city, it is not about being credited for or known for but the initiation of it had been by some other CM but it is presented as if it was established and conceived by Naidu which is far from reality and incorrect. Such events need clear presentation which is missing. Better to avoid them in the lead by elaborately mentioning them in the respective sections. ~ Chinnusaikrish (talk) 08:16, 16 February 2024 (UTC)
 * Sources attribute the project to Naidu in an unqualified way. According to the sources, it was his idea and the project was put into motion by his government, during his chief ministership. But you may be right, and it may not be so clear cut. But a reliable source is required to present this in a less-clear-cut way. It would be great if you would make the needed improvements to the body. What he did during his terms in both policy and politics is pretty weakly covered. —Alalch E. 08:33, 16 February 2024 (UTC)
 * Seems you mistook Cyber Towers to HITEC City. This project was envisioned by the then Central Congress Government with the inauguration by Rajiv Gandhi under the regime of former CM Janardhan Reddy. Under Naidu's regime several IT companies were fielded with further expansion in many areas. This was misproperly Rpresented as his vision and inauguration which has to be differentiated properly. Better to expand this in the respective section. efer - (https://www.sakshipost.com/politics/2018/12/05/a-timeline-of-cyberabad-history-fact-check-for-chandrababu-naidu )
 * And as I said before I'm going ahead with improving the body in a better way so that the facts and events may get presented true to the sense and Thanks for allowing me. ~ Chinnusaikrish (talk) 09:00, 16 February 2024 (UTC)

Have not assumed the office yet
Someone restore to the last incumbent office until 12 June immediately EntrepreneurPedia (talk) 07:26, 10 June 2024 (UTC)

title: Talk:N. Chandrababu Naidu


text:
User talk:Jeffrey Smith/Archive 1

Welcome
Hello there, welcome to the 'pedia! I hope you like the place and decide to stay. If you need pointers on how we title pages visit Naming conventions or how to format them visit our manual of style. If you have any other questions about the project then check out Help or add a question to the Village pump. Cheers! --maveric149

January 15 Seattle meetup
Just wanted to let you know we are planning another Seattle meetup on January 15, 2005. We're trying to get a sense of who will attend, so please drop by that page & leave a note. -- Jmabel | Talk 01:38, Dec 23, 2004 (UTC)

Stoicism
Thanks for picking up my carelessness. That'll teach me to edit after midnight. Mel Etitis ( Μελ Ετητης ) 11:16, 22 May 2005 (UTC)

User categorization
Greetings, Jeffrey Smith! Please accept this message as an invitation to categorize your user page in the category Category:Wikipedians in Washington and removing your name from the Wikipedians/Washington page. The page will be deleted when all users have been removed. Even if you do not wish to be placed in a category, could you take a moment to remove your name from the Wikipedians/Washington page? Thanks!!

To add your name to the category, please use the tag   to ensure proper sorting.

For more information, please see User categorisation and Category:Wikipedians by location. -- Roby Wayne  Talk •  Hist 04:30, 8 September 2005 (UTC)

Working Man's Barnstar

 * Wow, thanks! I'm pleased to be of service. — Jeff | (talk) | 11:35, 17 January 2006 (UTC)

Template talk:H2G2Researcher
Could you please read and respond to my comment on the bottom of this page? --    NERD42    [mailto:nerd42@gmail.com EMAIL ]  TALK  H2G2 UNCYC NEWS   23:57, 15 January 2006 (UTC)

 * Apologies for the delay. I'm replying right now. — Jeff | (talk) | 10:38, 18 January 2006 (UTC)

Birmingham, Alabama userbox
Mille grazie for catching the possibly bad image on this userbox. I'd just assumed a picture out of the city's article would be righteous. Good catch. MARussellPESE 02:41, 19 January 2006 (UTC)

Degree Userbox
Thanks :) Avi 13:09, 20 January 2006 (UTC)

Syntax for Degree Userbox
Thanks for fixing that on my userpage. Did the syntax recently change? Lawyer2b 15:29, 20 January 2006 (UTC)

 * I was the one who changed the syntax (after updating the user pages of everyone who used a degree userbox). The degree userboxes were made from the single, large, obfuscated {{User degree}} that used the {{switch}} tool to display the appropriate degree's userbox, given the degree's abbreviation as a parameter.  Under the new setup, each degree userbox has its own, separate, independent template; this is why I had to change the syntax on the user pages.  The old syntax was working fine (and was entered correctly at the time it was added), but it would have been broken after I made the change. — Jeff | (talk) | 11:23, 24 January 2006 (UTC)

 * Thanks from me, also. - WarriorScribe 17:21, 20 January 2006 (UTC)
 * I don't think I could ever go back to my old userbox ;-) Thanks! Michaël 18:01, 21 January 2006 (UTC)

Thanks as well from me. -Acjelen 17:38, 20 January 2006 (UTC)

Thanks also from me. Bduke 20:31, 20 January 2006 (UTC)

Thanks
for fixing the coding error on my page Ginar 17:06, 20 January 2006 (UTC)

for fixing the coding error on my page. It would have taken much more text to explain to me what needed to be done. Val42 16:34, 21 January 2006 (UTC)

WP:AUM
Sorry for moving the shortcut, I didn't realize it was a shortcut to the talk page (and I'd never seen one of those before, heh). =) And as a note, I modified your "new messages"-style header at the top since it seemed you were trying to duplicate the look of that (now it's identical except for your customized colors/text). =) Anyways, sorry again! —Locke Cole • t • c 04:14, 22 January 2006 (UTC)

 * I wasn't worried about it. FWIW, I don't think I've seen a shortcut to a talk page anywhere else either (probably a testament to how controversial the page is/was, that someone felt they needed to create a shortcut for easy access).  As for the message at the top of the page, that's actually subst'd from {{message}}. — Jeff | (talk) | 11:23, 24 January 2006 (UTC)

 * Ahh, cool. I updated that template then, hopefully nobody minds. =) And you're right about AUM being controversial; hopefully we can get everything squared away with it now that Brion is involved. —Locke Cole • t • c 12:05, 24 January 2006 (UTC)

Hye Jeff BL
Hye, so you asked me about the user box Bl...For me that mean Bachelor of Literature (In french we say "Bac Littéraire") so if you don't want to hurt someone, i think that the best way to resolve the problem is to do 2 user box and precise the different possibilities. Gxis jonathaneo

 * I have created {{User degree/BL}} and also updated your user page. — Jeff | (talk) | 11:23, 24 January 2006 (UTC)
 * Thanks jonathaneo

userboxes and subst
Listen, Jeffrey, I hate to sound like a total tyro here, but I don't get subst and how it effects the use of userboxes. For example, I use a number of userboxes. Should I, in my userpage, be putting subst inside the braces? What I am looking to do is whichever ways is seen as the best practice on wiki--Vidkun 16:03, 26 January 2006 (UTC)

 * Sorry that I'm just now answering this. If you're just an end-user of userboxes—that is, you use pre-made userboxes (like {{user separation}}) or you make your own for use on your page (like your Freemasonry userbox)—then subst isn't something you really need to worry about.  The main place where using subst is advised is if you're creating a new userbox template for others to use; so, for example, if you wanted to create the template {{user freemasonry}} for others to use, you might be advised to use subst in creating that template.  (It used to be that subst was enforced somewhat heavy-handedly, since Avoid using meta-templates was tagged as official policy and using subst was needed to bring userboxes in-line with the policy.  Now, it seems that meta-templates might not be as bad as once thought, so I don't think using subst is as important as it used to be.)  I hope this clears things up somewhat.  Let me know if you have further questions.— Jeff | (talk) | 07:54, 6 February 2006 (UTC)

thanks
Hey Jeffrey, thanks for dropping by my user page and updating one of my userboxes (the MA one). Not sure exactly what you did, but thanks anyway. Anytime! Penguin2006 08:33, 27 January 2006 (UTC)

Sig correction
Thanks so much for letting me know about that. I had changed the font color so I didn't immediately see that it pointed to an empty page. I didn't think to actually check it like any intelligent person should. If you hadn't left that message who knows how long I'd keep using the wrong link. Now that I know people actually pay attention to that thing, I'd better remove the tacky multicolors while I'm at it. =P —  Indi  [ talk ] 16:27, 6 February 2006 (UTC)

Regarding logos in Userboxes
Hello. Today I, on the advice of other users, changed the Opera Userbox to incorporate the official Opera Logo. You reverted with the claim that company logos should not be used in userboxes. However, there are copious numbers of userboxes with official logos in them. How do you account for this discrepancy? Please respond on my talk page. TydeNet 03:33, 20 March 2006 (UTC)

 * Followed up on user's talk.

thanks
thanks for the NiMUD edits King queermo 14:51, 9 June 2006 (UTC)

Userbox problem
Ancientanubis complains the removal of the images in his userboxes User Straw Hat, User Full metal alchemist, User NERV, and user Ghostintheshell2 because he claims that he legally owns the images. Here's the replies he gave me:

What can we do about this matter? I've already told him about the images, but it seems he still does not understand the "fair use" image policy on userboxes. Can you tell him for me ASAP? -上村七美 | talk 23:21, 19 June 2006 (UTC)

 * I've left him a message on his talk page that points to the explicit policy statement prohibiting fair-use images on user pages and explains some of the reasoning behind it. Hopefully, it will be well received.  Thanks for pitching in with the (sometimes controversial) task of keeping fair-use images out of userboxes.  — Jeff | (talk) | 10:10, 20 June 2006 (UTC)

 * Thank you for the help Jeff... sometimes it seems that when someone takes time to explain it them selves instead of just referrin you to a page with a list of rules.... well lets just say it makes me feel more willing to cooperate and understanding the bigger picture.

 * thank you again for taking time to help me understand the whole situation
 * --Ancientanubis 01:54, 21 June 2006 (UTC)

Linking
hey jeff... this may come as a stupid question at first glance but bare with me

i'm trying to set up a link on a page so that there isn't a bit (blah blah blah) right after the link explaining more about the item being linked

what i was seeing if i could do was have it explained within the lil box that appears under a link when you hold your mouse over it(idk the technical term but i've seen it refured to as simply a title)

 * ie, lookin at my talk page link for example are the way's i know how to do links w/in wikipedia

 * that is what i'm tryin to change

i looked in the editing help section for link's and i couldn't find anything in there(i think)

is there something i am overlooking or is it just not possible w/in wikipedia at this time??

respond when you get a chance, thanks, Ancientanubis 19:09, 21 June 2006 (UTC)

 * I think text (appears as: text ) would do what you want, where foo is what you want it to say in the mouseover box/title.  For example:

 * I can't think of a good reason to use titles like this in encyclopedia articles, but it's probably fine to use on your user pages and talk pages. Hope this helps. — Jeff | (talk) | 08:58, 23 June 2006 (UTC)

crazy question
hey jeff, long time no see

i have a quick(kinda weird) question

have you ever heard of a program that you could copy and paste wiki format into, then be off line and it'll read it as if it were an actual wiki article so you could work on edits offline

if that doesnt make sence let me know and i'll explain it a bit further:P --Ancientanubis 21:46, 14 August 2006 (UTC)

WikiProject Disambiguation Talk Request
This is a form message being sent to all WikiProject Disambiguation participants. I recently left a proposed banner idea on the WikiProject Disambiguation talk page and I would appreciate any input you could provide. Before it can be approved or denied, I would prefer a lot of feedback from multiple participants in the project. So if you have the time please join in the discussion to help improve the WikiProject. Keep up the good work in link repair and thanks for your time. Nehrams2020 21:31, 9 October 2006 (UTC)

Change to Common.css
Per recent discussions, the way in which Persondata is viewed by Wikipedia editors has changed. In order to continue viewing Persondata in Wikipedia articles, please edit your user CSS file to display table.persondata rather than table.metadata. More specific instructions can be found on the Persondata page. -- ShakingSpirit talk  on behalf of Kaldari 01:15, 25 December 2006 (UTC)

title: User talk:Jeffrey Smith/Archive 1


text:
User talk:Tengai~enwiki

Hello there, welcome to the 'pedia! I hope you like the place and decide to stay. If you need pointers on how we title pages visit Naming conventions or how to format them visit our manual of style. If you have any other questions about the project then check out Help or add a question to the Village pump. Cheers! --maveric149

Note to myself: Tried to fix Lunation Number ... maybe later, maybe not. -- Tengai 17:35, 13 March 2007 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Tengai. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Tengai~enwiki that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name. If you think you might own all of the accounts with this name and this message is in error, please visit Special:MergeAccount to check and attach all of your accounts to prevent them from being renamed.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 03:18, 20 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 19:34, 22 April 2015 (UTC)

title: User talk:Tengai~enwiki