Talk:Limit

AoPSWiki Article of the Day
Limit was the AoPSWiki Article of the Day for January 6th, 2008

Hello. I hastily created this article because I noticed we didn't have one on limits. I plan to add things such as proofs for uniqueness, multiplication, and addition, as well as stuff about continuity, left- and right-hand limits, infinite limits, continuous functions, etc., etc., etc. Please contribute if you'd like.

The article looks great. By the way, when you add something to a "Talk" page, add a "signature with time stamp" so everyone knows who said that. The code is two dashes (-) followed by four tildens (~).

--Xantos C. Guin 21:15, 29 June 2006 (EDT)

Oh, sorry; I thought everybody else could see it. That was me, by the way. Also, sorry about that stupid mixing-up of $\delta$ s and $c$ s. --~~

Whoops; I thought you had written "two tildes." All of the anonymous comments above were written by me. --Boy Soprano II 17:44, 30 June 2006 (EDT)

The "Existence of Limits" section needs work. (In particular, I think $f(x) = \frac{1}{x}$ is a bad example to start with -- $f(x) = \lfloor x \rfloor$ would be better.) Also, there is no mention in this article of infinite limits or limits to infinity, both of which are important. --JBL 14:41, 7 January 2008 (EST)

Regarding the limit of the function $f(x)=0$ for $x \ne 0$ and $f(x)=1$ for $x=0$ .

This function doesn't have a limit at x=0. Proof: Pick $\epsilon = 1/2$ . There is no $\delta>0$ such that $|x-0|<\delta \implies |f(x)-0| < 1/2$ . For any $\delta$ that you pick I can pick $x=0$ and $|f(0)-0|>1/2$ . Jep 00:15, 7 May 2008 (UTC)

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Talk:Limit