Difference between revisions of "Talk:Limit"
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The "Existence of Limits" section needs work. (In particular, I think <math>f(x) = \frac{1}{x}</math> is a bad example to start with -- <math>f(x) = \lfloor x \rfloor</math> would be better.) Also, there is no mention in this article of infinite limits or limits to infinity, both of which are important. --[[User:JBL|JBL]] 14:41, 7 January 2008 (EST) | The "Existence of Limits" section needs work. (In particular, I think <math>f(x) = \frac{1}{x}</math> is a bad example to start with -- <math>f(x) = \lfloor x \rfloor</math> would be better.) Also, there is no mention in this article of infinite limits or limits to infinity, both of which are important. --[[User:JBL|JBL]] 14:41, 7 January 2008 (EST) | ||
| − | Regarding the limit of the function <math>f(x)=0 for x \ne 0 </math>and <math>f(x)=1</math> for <math>x=0</math>. | + | Regarding the limit of the function <math>f(x)=0</math> for <math>x \ne 0 </math>and <math>f(x)=1</math> for <math>x=0</math>. |
| − | This function doesn't have a limit at x=0. Proof: Pick <math>\epsilon = 1/2</math>. There is no <math>\delta</math> such that <math>|x|<\delta \ | + | This function doesn't have a limit at x=0. Proof: Pick <math>\epsilon = 1/2</math>. There is no <math>\delta>0</math> such that <math>|x-0|<\delta \implies |f(x)-0| < 1/2</math> . For any <math>\delta</math> that you pick I can pick <math>x=0</math> and <math>|f(0)-0|>1/2</math>. [[User:Jep|Jep]] 00:15, 7 May 2008 (UTC) |
Revision as of 19:46, 6 May 2008
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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 
s and 
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 
is a bad example to start with -- 
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 
for 
and 
for 
.
This function doesn't have a limit at x=0. Proof: Pick 
. There is no 
such that 
. For any that you pick I can pick and 
. Jep 00:15, 7 May 2008 (UTC)
