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When we talk about: $$\lim_{x\to{c}}f(x)=L.$$ Is there a formal name for the number "$c$"?

I know that the notation means "$L$ is the limit of $f(x)$ as $x$ approaches $c$". It just would be nice to be able to refer to "$c$" separately without saying "what $x$ approaches". I tried to look at various textbooks but didn't find anything.

Xander Henderson
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Ari
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    I am not aware of a standard terminology. – Steven Gubkin Feb 05 '20 at 20:13
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    Just for fun: The "approachand," pronounced ah-proach-and, analogous to "operand." – Joseph O'Rourke Feb 06 '20 at 00:36
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    I generally refer to it as "the limiting value of $x$". It is a little clunky, and probably not any better than "the thing which $x$ approaches", but works. – Xander Henderson Feb 06 '20 at 02:21
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    Maybe "approach value" for $c$ and "limit value" for $L$? – Dave L Renfro Feb 06 '20 at 19:16
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    @JosephO'Rourke I believe the "correct" term based on Latin would be "appropiand" (that which is to be approached). – user1815 Feb 07 '20 at 00:30
  • @BrendanW.Sullivan Isn't the "f(x)" called function? – Pedro Feb 26 '20 at 14:19
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    Maybe, we could refer to $c$ as the limit point because, in the definition of limit, $c$ has to be a limit point of the domain. This expression would be good because, according to the general definition, a limit point of the domain is a point that (i) can be approximated by elements of the domain and (ii) need not be in the domain (which are the two properties of $c$ that have to be highlighted for the students). – Pedro Feb 26 '20 at 14:54
  • "Center of the limit"? – Peter Saveliev May 28 '20 at 15:59
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    I was about to suggest the same as @Pedro and wanted to add, some might get potentially confused and stumble wondering whether limit point refers to $c$ or $L$ but one thing I try to do to subconsciously reinforce a distinction is to refer to "points" in the domain and "values" in the range (as consistently as I remember, and when e.g. you compose one function into another the terminology plays not so well, but I want to think it helps). – Vandermonde May 28 '20 at 18:44
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    If you are proposing an answer to the question, please consider leaving an answer, instead of a comment. Comments that are mini-answers have several issues: they cannot have their own comment threads, they dissuade others from posting answers, they cannot be voted on, and they cannot be accepted. – Chris Cunningham May 28 '20 at 19:16
  • I've always heard the phrase "limit of $f$ at $c$", so one could refer to $c$ in this indirect way. If I find the time to locate it in the literature, I'll leave it as an answer. – Michał Miśkiewicz Aug 16 '23 at 19:45

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I vote for Pedro. We should call the point at which the limit is taken the limit point. In contrast, the value obtained by the limit (if it exists) is the limit's value. In particular, $$ \lim_{x \rightarrow c} f(x) = L $$ has limit point $c$ and the value of the limit is $L$. This terminology keeps with the usual usage of the term value for outputs of the function. In addition, while the term limit point does have a more abstract topological definition, I don't think there is much danger of confusion.

James S. Cook
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The "c" in limit notation is called the index (or at least that's what I have always been taught).

Plant
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Not standard but how about: the limit of $x$ or the limit of the independent variable?

Michael Bächtold
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