Talk:Limit (mathematics)/Archive 1

useless
this page is GREAT for people with a firm grasp of calculus concepts, but it SUCKS if you are trying to actually LEARN something here. i thought wiki was a place to learn, not a place to show that you are more learned than those who read your articles. thanks for nothing. —Preceding unsigned comment added by 72.241.143.189 (talk) 23:01, 14 June 2010 (UTC)


 * You've misunderstood the purpose of Wikipedia. It is an encyclopaedia not a textbook. This is one of the points in What Wikipedia is not. There's some textbooks being set up at wikibooks but using google to find something on the web might be best. Dmcq (talk) 23:28, 14 June 2010 (UTC)


 * I have a mathematics degree and I agree with 72.241.143.189. For starters, the first paragraph defines limit in terms of two more advanced concepts that have not been introduced, "Complete space" and "Cauchy series".  That's poor exposition in either an encyclopedia or a textbook. CharlesTheBold (talk) 23:40, 20 February 2011 (UTC)
 * WP:MOSINTRO specifically states that "specialized terminology and symbols should be avoided in an introduction." Ndanielm (talk) 03:12, 4 November 2011 (UTC)

I have a mathematics degree and I agree entirely with 72.241.143.189 and CharlesTheBold. It just saddens me that someone might come to this page genuinely wanting to know what a "limit" is and be bewildered and disgusted at sentence two after encountering such incomprehensible math gibberish as "define a new point from a Cauchy sequence of previously defined points within a complete metric space."

What if instead of that nonsense we took a genuine shot at explaining what is so awesome about limits in approachable language almost everyone could understand? What if we told by example and allegory and actually got through to someone why a limit is so amazing and useful? Then near the bottom half of the page we could start throwing in the technical math terms for those who want to know the details.

In history articles we don't require an intense in-depth knowledge of the time period to understand sentence two, why should we require 8 years of study to understand math articles? Again, I have a math degree and losing me in math gibberish at sentence two is just too high a standard for any written work, and completely goes against Wikipedia's mantra of "knowledge for everyone." 98.253.237.75 (talk) 02:54, 31 January 2012 (UTC)
 * I've deleted "sentence two" (the bit about Cauchy sequences)&mdash;I agree that it's too heavy for the lead section. You're welcome to make constructive suggestions about how to improve the rest of the article, or even have a go at editing it yourself.  Thanks for the feedback so far. Jowa fan (talk) 03:16, 31 January 2012 (UTC)

"gets close to"
Shouldn't this be "approaches"? —Preceding unsigned comment added by Fimbulfamb (talk • contribs) 00:09, 4 May 2008 (UTC)

One sided and unbounded limits
What about limits in R when you go from right and from left side of the point p? The general limit the article is talking about doesn't have to exist (e.g. lim_(x->0+)(ln(x)) can be calculated (0+ means from right) while lim_(x->0-)(ln(x)) isn't defined in R). INAM, but I think it should be explained in the article. Thanks.

is it an "unbounded limit" or "limitless because it is unbounded"? Pizza Puzzle


 * To be honest, I'm not sure what you mean... If f(x) tends to infinity as x tends to c, then f(x) is unbounded in any neighbourhood of c. I would say that it has no limit, because infinity isn't really a "limit" as such... Unless, of course, you define it to be one... (cf. Dumpty, 1871) -- Oliver P. 21:29 3 Jun 2003 (UTC)

Well, what i mean, is that u changed this article to state that something had a "limit of infinity" - ill fix it. Pizza Puzzle


 * No, I didn't say anything about anything having a "limit of infinity". I did, however, say that a function can have a limit as its argument tends to infinity. Admittedly, what I added was not particularly well written, but it didn't say what you seem to think it said. -- Oliver P. 15:42 8 Jun 2003 (UTC)

Actually, when the limit is "infinite", it means the function is actually limitless at that point. It even fits semantically. I'm actulally having nightmares right now with limits since my partials include the demonstration of limits, which are a total pain Hearth 02:19, 3 March 2006 (UTC)

l.i.m.
In several mathematical books published more than 50 years ago not only (symbol) "lim" but also "l.i.m." is used. What does it mean?
 * Um, can you give an example? I don't think it means "limit".  71.141.234.189 08:12, 11 February 2006 (UTC)

Oscillating Limits
Consider Grandi's alternating series

$$\sum_{n=0}^\infty (-1)^n$$

The sequence of partial sums would thus be

$$1$$,$$0$$,$$1$$....

Isn't the limit oscillating ... why do we say it is divergent or not convergent. Do we really have a concept of oscillating limits?
 * According to the conventional definition of limits, this does not converge. Convergence of the sequence of partial sums ak means that for any epsilon, there are numbers L,M so that for all terms ak for k > M, |ak - L| < epsilon.
 * Consider epsilon=1/3, obviously there is no number L so that all of the partial sums are eventually within epsilon of L. Phr 00:23, 4 April 2006 (UTC)

Oscillating limits... never heard of that one I got scammed 05:22, 22 October 2006 (UTC)

Pushing it to the limit
I added a vandalism warning for for all the 'push it to the limit' jokers, I doubt it will help much, but you never know. --N******* 21:04, 14 July 2006 (UTC)

(moved from above) Hey, when I go to this page (http://en.wikipedia.org/wiki/Limit_%28mathematics%29), I get a message that reads ''Welcome to Wikipedia. We invite everyone to contribute constructively to our encyclopedia. Take a look at the welcome page if you would like to learn more about how to contribute to our project. Unconstructive edits are, however, considered to be vandalism, and if you continue making these kind of edits you may be blocked from editing Wikipedia without further warning by a Wikipedia administrator. Please try making edits that improve, rather than damage, the hard work of others; I sincerely hope that you will do so. Should you have any questions relating to Wikipedia editing, please do let me know. Thank you.'' I didnt even edit this page! Why am I getting near-banned for vandalism? Once I figure out why I see this message when I go there, Ill delete this paragraph I just typed --RETROFUTURE 01:28, 18 July 2006 (UTC)


 * Because N******* added a vandalism warning to the article itself. Needless to say, that was a bad idea. Melchoir 03:15, 18 July 2006 (UTC)

is this an error or did i make a mistake?
Consider as x approaches 2. In this case, f(x) is defined at 2 and equals its limit of 0.4:

f(1.9) f(1.99) f(1.999) f(2) f(2.001) f(2.01) f(2.1) 0.4121 0.4012 0.4001 0.4  0.3998 0.3988 0.3882

why would it not be defined at f(2)? couldn't you just plug 2 in an end up with 2/5. 131.156.225.29 17:45, 18 September 2006 (UTC)

never mind, i think its been fixed 131.156.225.29 17:47, 18 September 2006 (UTC)

Nets
If at all, I think the notion of a topological net should be discussed as a subsection of the "limit of a sequence" portion here, as the net is the generalization of a sequence for a space that is not metrizable. Anyone? --King Bee 21:57, 31 October 2006 (UTC)

Higher-dimensional derivatives
Shouldn't note be made of limits in higher dimensions? Especially in 3-d (shrinking disc and such).EunuchOmerta 07:20, 30 December 2006 (UTC)

Limit under a filter
How about the description introduced by H. Cartan? The general notion of convergence is discussed in Filter (mathematics) but not directly mentioned is the very notion of 'limit'.Lightest 18:54, 13 February 2007 (UTC)

formula writing and intelligibillity
this way f(x) = \frac{x}{x^2 + 1} " of writing math formulas doesn't help understanding the explanation. Is it possible to find a basic explanation for this kind of language? 89.1.244.26 13:12, 20 March 2007 (UTC)


 * This is the alt text. Most people won't see the alt text, they will see the PNG image (which is much more readable). The alt text is currently just TeX code. It would be possible to make it more readable, at least in some cases, but I don't know if any developers are working on this. --Zundark 14:00, 20 March 2007 (UTC)

Rules part
The rules mentioned are very similar to those on Limit of a function, and I really dont think they belong here. Especially when they are not as formal as on the other article. Paxinum (talk) 15:06, 24 November 2007 (UTC)


 * I agree, this article should be rewritten so that it simply points readers to different uses of limits in mathematics. Akriasas (talk) 02:12, 15 December 2007 (UTC)

why can't delta = 0 ?
just wondering... BriEnBest (talk) 20:46, 24 November 2007 (UTC)


 * Well, delta can be 0, but it is sufficent for the property to hold for positive values. If it was neccesary for delta=0 to hold, then the definition is useless, because the function needs to be defined in the point where one wants to calculate the limit. I.e $$\lim_{x\rightarrow 0^+} 1/x $$ could not be calculated, since 1/0 is not defined. Paxinum (talk) 11:13, 15 December 2007 (UTC)

Vandalism?
Whats this? the limit is the intended brickjee of a function Suppose ƒ(x) is a real-valued function and c is a real number. The expression: ... brickjee? What the heck is a brickjee? 76.90.9.68 (talk) 07:53, 13 June 2008 (UTC)


 * I have reverted the corresponding change. —Tobias Bergemann (talk) 08:03, 13 June 2008 (UTC)

the definition of a limit
$$\lim_{x \to \infty} f(x) = L$$ if and only if for each ε > 0 there exists an S such that $$|f(x) - L| < \varepsilon$$ whenever x > S.

the current definition of a limit doesn't cover todd's evil limit


 * $$\lim_{n \to \infty}(n\sin(2\pi*e*n!))=2\pi$$

there is no ε for which you can say the above is true - the equation swingins between plus and minus \infty but if you look at the taylor series approximation to sin and e, you find that that the limit is true.

however for any ε<1 you trivially find that no value the definition of limit above is true. (err, and sorry about the bad maths formatting, i'm unsure how to do it correctly) Andy t roo (talk) 07:03, 9 March 2009 (UTC)
 * I tried to fix the formatting, but it is not clear to me what you mean. Did you mean $$e^{n!}$$?  If we are just multiplying by e I don't see how the taylor series for $$e^x$$ makes any difference.  I also changed the limit so it was as $$n\to\infty$$.  It seems to me that "todd's evil limit" doesn't exist. Thenub314 (talk) 08:40, 9 March 2009 (UTC)


 * Based on a web search, "Todd's evil limit" is $$\displaystyle \lim_{n \to \infty} n\sin(n\cdot e \cdot n!)$$. This is the limit of a sequence, not the limit of a real-valued function. So, Andy, you would need to turn to the section of this article that talks about limits of sequences. &mdash; Carl (CBM · talk) 10:46, 9 March 2009 (UTC)

Useful illustration?


Useful? Or not? Algr (talk) 21:35, 6 April 2009 (UTC)


 * It's amusing, but I don't see how it aids in the understanding of what a limit is. --Zarel (talk) 22:33, 6 April 2009 (UTC)
 * Zarel followed me here from another article. How about letting the locals decide.  Algr (talk)
 * It's just yet another indication that you have no idea what the concept of a limit is. Unless you'd like to clarify your point.
 * This might be a useful illustration of perspective, though. Too bad it's already well illustrated there. --72.177.97.222 (talk) 23:51, 6 April 2009 (UTC)
 * I knew Wikipedia has a silly trend of people "owning" articles, but I never knew it was official policy that I wasn't allowed to comment on articles I don't regularly comment on. --Zarel (talk) 06:39, 7 April 2009 (UTC)
 * I don't think the illustration helps, it is not encylopedic and is confusing mathematically. --Salix (talk): 07:07, 7 April 2009 (UTC)

Allow me to summarize the consensus, in case it is unclear to you, Algr:

No.

My recommendation would be to read the article instead of commenting here on the talk page. Come on; take a crack at it. You might learn something. --72.177.97.222 (talk) 13:02, 8 April 2009 (UTC)
 * A consensus of one. I apologize to the locals, I didn't mean to bring my fan club here. Algr (talk) 17:56, 10 April 2009 (UTC)
 * I hate to break this to you, Algr, but it appears that... there are no locals. Take a look at the history of this page. Do you see evidence of repeat visitors? Salix has made two other contributions in the last 3 years. That hardly classifies him as a "local", and certainly not in the same way that we are locals to 0.999...
 * And it's a consensus of three.
 * Now read the article already! --72.177.97.222 (talk) 12:29, 11 April 2009 (UTC)


 * I agree with Salix.. Paul August &#9742; 01:46, 11 June 2009 (UTC)

"In this case, as x approaches 1, f(x) is undefined (0/0) at x = 1 but the limit equals 2:"
It is incorrect to say f(x) is undefined as x approaches 1. Zero over zero is the indeterminate form which means you have to simplify. In this case, the simplification involves multiplying by conjugate pairs, so that you get (x^3/2 - x^1/2)/(x-1) + (x-1)/(x-1) which reduces to x^1/2(x-1)/(x-1) + 1 -> x^1/2 + 1. Substitute x = 1 in this reduced form and f(c) = 2. Therefore, x = 1 is a hole in the graph, not a vertical asymptote, and not undefined for the reason specified in the article. Can someone with the wiki skills please correct this? It'd be much appreciated, thanks! —Preceding unsigned comment added by Shfauzia (talk • contribs) 05:55, 26 May 2009 (UTC)


 * It's perfectly fine to say that f(x) is undefined as x approaches 1. 0/0 is the indeterminate form, which is undefined unless you're looking at limits (which is why the function is undefined, but its limit is defined). You are correct in that x=1 is a hole in the graph and not a vertical asymptote, but holes in graphs are by definition undefined - if it were defined, there wouldn't be a hole there. --Zarel (talk) 04:30, 11 June 2009 (UTC)

Does the limit of 1/x as x tends to 0 exist?
In regard to the latest edit: the reason I used parentheses in the sentence
 * "The following rules are valid if the limits on the right hand side exist (and are finite)."

is that many authors use the phrase "the limit exists" to include the statement that it is finite; i.e., when a limit is infinite, they say that the limit does not exist. Given this, are there any objections to putting the parentheses back? Ebony Jackson (talk) 01:38, 11 June 2009 (UTC)


 * It is fine to put them back, it is really just a minor matter of style, and your way is certainly as good as mine. Since I was the one to take them out I'll save you and put them back now. Thenub314 (talk) 13:11, 11 June 2009 (UTC)


 * OK, thank you. Ebony Jackson (talk) 04:11, 13 June 2009 (UTC)

"Change in the formal definition"
It read forall epsilon there exists delta forall x (0<|x-p| |f(x)-L|0 there exists delta>0 such that 0<|x-p| |f(x)-L|0 there exists delta>0 such that forall x in (p-delta, p+delta)\{x}  |f(x)-L|<epsilon

not both.

By the way if this is true:

(0<|x-p| |f(x)-L|<epsilon)

then surely this is true:

forall x (0<|x-p| |f(x)-L|<epsilon)

and vice-versa. —Preceding unsigned comment added by 132.204.254.45 (talk • contribs) 22:07, September 23, 2009


 * Absolutely wrong. Outer quantifiers can sometimes be removed, but not inner quantifiers.  — Arthur Rubin  (talk) 18:44, 24 September 2009 (UTC)

Revert of redirect to Limit
This article was recently redirected to Limit. I reverted since I think these needs discussing. See also the discussion here. Paul August &#9742; 15:11, 28 November 2009 (UTC)


 * Alright, I was the one who did who redirected it. The problem is that this article was basically a less developed version of limit of a function with a bit of limit of a sequence and a few comments about possible other uses. I think that this page needs to be more focused. If it remains it seems like it should cover the idea of a limit in mathematics and clearly note that it is not the main article for either limit of a function or sequence. I'm working on cleaning it up and have included a hatnote to that effect. Let me know what you think. Cheers, — sligocki (talk) 00:27, 4 December 2009 (UTC)


 * I've been WP:bold and slashed a lot from this article and because of several issues I've noted, I pushed this article down to C-class. But, let's see if we can't develop it up to an A-class article! Cheers, — sligocki (talk) 01:25, 4 December 2009 (UTC)

Error in "Limit of a function"
I've tried to correct that $$f(x) = \frac{x^2 - 1}{x - 1}$$ is not undefined at f(1).  $$ \frac{x^2 - 1}{x - 1} = \frac{(x + 1)(x - 1)}{x - 1} = (x + 1) $$  which 1 + 1 = 2, therefore, not undefined. I've attempted to correct this with $$ \frac{1}{x - 1} $$, but it has since been reverted. --Unrealomega-1 (talk) 07:56, 12 January 2010 (UTC)


 * I don't know what the 1/(x-1) business is about and am ignoring it.
 * The expression is only defined at x=1 because of the limit definition. Possibly using some other expression where it wasn't so easy to do the division would be better as an example. Canceling out the (x-1) factor above and below is only allowed when x is not 1, what one can say is that the expression is (x+1) when x is not 1. The value when x=1 is given by the limit definition. If you try calculating it on a calculator you'll see it correctly complains about a divide by 0.
 * The example might be easier with something like (ex-1)/x at 0 where people can't go automatically dividing. Dmcq (talk) 10:38, 12 January 2010 (UTC)


 * The user "Unrealomega-1" is correct: the function provided as an example is not undefined at f(1). You merely factor the numerator and divide. I would suggest using a function such as that shown in http://en.wikipedia.org/wiki/Limit_of_a_function . But this needs to be changed: it is wrong as it is currently written. 129.82.228.174 (talk) 19:17, 27 January 2011 (UTC)


 * On the contrary, it's 0/0 at x=1. Some people consider factoring or elimination of a removable singularity to be done automatically, but this is not defined at x=1.  — Arthur Rubin  (talk) 19:58, 27 January 2011 (UTC)


 * As it relates to limits, this goes to the intermediate form 0/0, which can then be solved easily using L'Hospital's rule. As a function, it is obviously equal to something that is defined at f(1) (as Unrealomega-1 said). That's okay, though.  The proud people who maintain this article shouldn't be compelled to replace a potentially-confusing example with a clear and accepted one from another article. 129.82.228.174 (talk) 01:26, 4 February 2011 (UTC)
 * What "clear and accepted one"? We can argue about "potentially confusing"&mdash;as you're obviously confused, the potential must exist somewhere. But "clear and accepted one"?  — Arthur Rubin  (talk) 03:00, 4 February 2011 (UTC)


 * I notice that the example is the first illustration of a limit. The example does happen to be a bit artificial, which may confuse a novice.  How do people feel about replacing it by, say, $$x^x$$ or some other function where the singularity is somewhat less obviously removable?  Tkuvho (talk) 10:57, 4 February 2011 (UTC)

Limited infinity
Infinity relates to both basic elements of our reality those of space and time. Infinite space is unlimited magnitude when related to a point. In relation to time infinity means unlimited flow of time in the past and in the future. Magnitude does not apply to time because time is change of velocity of rotation of a point. The medium of space time consists of variable units within limited intervals of time. The units, which manifest the laws of nature, interact and cause change when motivated. The equation below shows the basic organization of space time. ∞	                                                     O <  Σ 1/2n  < 1 n=1 The equation shows that the two static limits of ‘0’ and ‘1’, contain between them, infinite plurality of space times. Neither ‘0’ nor ‘1’ can be reached. This means that neither Nothingness nor static state exist. There is no ‘beginning’ or ‘end’ of a space time. The ‘beginning’ is not the Nothingness of’0’. It is the ‘1’ duality of (0<1). Each interval of (0<1) is within itself and it contains itself. Each unit 1/2n is a different space time and each contains infinite plurality in (1/2n>1/2oo-1). The units are imperfect images of the equation. When there is nothing within (0<1) the infinity is static Nothingness. The imbalance between any two adjoining units motivates transformation from ‘0’ to ‘1’. An observer ‘1’, who is located at a point 1/2g always sees the same organization of the medium.

2n(1/2g) >2(1/2g)>1(1/2g)>1/2(1/2g)>1/2n(1/2g)

At a point in which observer’s unit of measurement of velocity of the flow of time 1/2g is identical with 1/2n of the medium there is a boundary of the observer’s space time. Beyond that boundary there is a different space time in which observer’s unit of consciousness, measuring velocity of flow of time is 1/2g+1. What varies is the observers unit 1/2g of consciousness which measures the space time. It is therefore the observer who creates variation in the organization of this invariable eternal medium of Nothingness. KK (83.28.204.145 (talk) 14:51, 4 June 2010 (UTC))


 * I would say that this is totally wrong, and unrelated to the article, but it's possible there's something there I don't understand. — Arthur Rubin  (talk) 15:32, 4 June 2010 (UTC)

1st fig needs changing
The figure has c, but both the caption and the article use p. —Preceding unsigned comment added by 76.115.3.200 (talk) 03:23, 8 June 2010 (UTC)

Important example, should be in artcle
lim x -> 0, (1/x)^r where 0<r<1, does this converge —Preceding unsigned comment added by 173.206.84.108 (talk) 02:29, 15 November 2010 (UTC)

No, it doesn't converge. For fixed r, (1/z)^r  becomes arbitarily large as x approaches 0.CharlesTheBold (talk) 23:40, 20 February 2011 (UTC)

Limit of a sequence
I have undone Arthur Rubin's revert of my edit, because he has not, to my satisfaction, provided adequate reasons for his revert. The key reasons he does give are 'unnecessary and confusing generaliztion'.

For a start, the additional mathematical information that I am inserting is not confusing at all for any mathematically literate reader. It may be slightly tricky for anyone who isn't mathematically minded, but if we're rejecting material on that basis, then we should probably delete this whole page!

Secondly, and far more importantly, I would ask the said editor by what objective criteria he comes to the conclusion that a piece of factual mathematical information is 'unnecessary' for an encyclopedia. For not only is the said information factually accurate, but it is also extremely important, since it gives the full picture of the relationship between limits of sequences and limits of functions. Indeed, I would argue that it is the text as it currently stands which is confusing, since it fails to make clear that the reason f(x + 1/n) converges to the limit of the function at x is precisely because the sequence x + 1/n converges to x.Telanian183 (talk) 22:47, 6 April 2011 (UTC)


 * I can see a point to your generalization, but you missed a serious error. I've partially corrected it.  I just noticed another correction required.  — Arthur Rubin  (talk) 07:02, 7 April 2011 (UTC)


 * There is no serious error. There was a relatively minor one in that I had failed to specify that the sequence is not  allowed to be equal to the limit at any point, but that is (relatively) trivial and easily fixed.

Other than that however, what I said was perfectly correct. To back this up, I invite you to consider the following university lecture notes:

http://www.maths.ox.ac.uk/courses/course/12498/material

Clicking on the first pdf article (the one which says final draft) and scrolling down to Theorem 1.5.7 will bring you to the relevant material.Telanian183 (talk) 07:27, 7 April 2011 (UTC)


 * As you well know, course notes are not considered a reliable source; and the reals form a topological group, so an → x is equivalent to an &minus; x → 0, and the statement generalized becomes 1/n → 0, which seems simpler than x + 1/n → x. But that is trivia.  I'm just pointing out that your latest change is a style change, rather than a substantive change.  — Arthur Rubin  (talk) 07:39, 7 April 2011 (UTC)

true or false definitions
The sentence "Note that the above definition of a limit is true even if f(c) ≠ L." is in error. A definition is NEITHER true NOR false. A definition is just a definition. Statements could be true or false. What is the statement there?178.48.168.232 (talk) 09:09, 22 July 2012 (UTC)

Convergence and fixed point
This bit seems a bit sloppy. "A formal definition of convergence can be stated as follows." Yet, the next sentence says "Suppose { {p}_{n} } as n goes from 0 to \infty is a sequence that converges to a fixed point p " even though the formal definition of convergence has not been stated. As far as I can tell, the pieces of the intended definition are there, but they are not put together correctly. Later on there is another very confusing passage. "Given a function f(x) = x with a fixed point p ," If find this confusing because for the function f(x)=x, every point is a fixed point by definition. So step 1: "Check that p is a fixed point." confuses me quite much. -- Jonathan — Preceding unsigned comment added by 136.159.160.240 (talk) 16:56, 25 July 2012 (UTC)

Nonsensical passage
One passage in the article reads:

"Note that the above definition of a limit is true even if f(c) ≠ L. Indeed, the function f(x) need not even be defined at c. For example, if f(x) = (x2 - 1)/(x - 1), then f(1) is not defined (see division by zero) . . .."

First of all, a mathematical definition is neither true nor false; it is a decision to associate a specific term or notation with a specific meaning. It would be better to say "Note that the above definition does not require f(c) = L." Or "Note that the above definition of a limit is valid even if f(c) ≠ L."

Secondly, the assertion that "f(x) = (x2 - 1)/(x - 1)" does not even make sense at x = 1 for a single-valued function f (precisely because the right-hand side, as 0/0, is not defined). So f cannot be mathematically defined as "not defined" for x = 1 by a mathematically meaningless statement. It must be stated what the domain of definition of f is.

Suggestion: For the example, stick with the original idea that f is defined at c but unequal to L. And define f(x) by (x2 - 1)/(x - 1) for x ≠ 1, and by f(x) = 17, say, for x = 1.Daqu (talk) 06:16, 14 November 2012 (UTC)

Archiving
Does anyone have an objection if I set up MiszaBot to archive threads on this page which are 3 or more months old? Callanecc (talk • contribs • logs) 07:36, 4 September 2012 (UTC)
 * I've set it up with archiving for threads which are at least 90 days old. Callanecc (talk • contribs • logs) 07:04, 6 September 2012 (UTC)

Yeah, I object strongly. Why are you making a discussion disappear so fast? It's not as if we're running out of space here.Daqu (talk) 20:57, 20 November 2012 (UTC)

Defined function at a division by zero
The article says a division by zero makes a function "not defined" at a point, and gives (x^2-1)/(x-1) as an example. This is not accurate. That function is very well defined, it is the function (x+1). There is no mystery. -- NIC1138 (talk) 04:44, 23 October 2012 (UTC)


 * One cannot perform the division (x^2-1)/(x-1) = x+1 when x=1, because then the denominator x-1 is equal to 0.  It's not quite accurate to say that the function itself is not defined (see my comment in the next section), but rather that the expression (x^2-1)/(x-1) is not defined, at x = 1.Daqu (talk) 21:06, 20 November 2012 (UTC)

standard part or "standard part"
A recent change to the section "limit as standard part" introduced quotation marks around "standard part" in the title of the section. I have no particular opinion on this other than conforming with wiki guidelines. Other than that, "standard part" and "standard part function" are by now standard terminology, and putting them in quotation marks may not make any more sense than putting "function" in quotation marks. If other editors care to comment we can see if a consensus can be found. Tkuvho (talk) 08:42, 25 December 2012 (UTC)

Math humour: You should change L to LL, for the latin nomer of double L.
The function would read.

For any x close enough to see, the limit will tend to ´ella´, instead of L (el).

Just to make sure that the female approach is correct, an ex being an ex.

Math humour.

The formulation as it is now,

When the ex is close enough to see, the limit will tend to him. (to many social examples to not be factual).

When the ex is close enough to see, the limit will tend to her. (Again, MANY a social example to not be factual).

Theological aspect (also humourous): God is a woman, not a male, ël is male, ëlla is female. (ohh, and jesus is his sister, ehhh, her sister). — Preceding unsigned comment added by 186.94.185.159 (talk) 15:53, 8 May 2013 (UTC)

The abbreviation lim
Isn't "lim" an abbreviation for limes (Latin) and not limit as the page suggests. "limit is usually abbreviated as lim"? It sounds very arrogant to write that it is a short for limit when it is clearly not. --Immunmotbluescreen (talk) 18:45, 14 June 2013 (UTC)


 * "Very arrogant" seems over-dramatic. If the abbreviation came into use in Latin during the appropriate era (as it probably did), then feel free to cite a source and change it. —&#91;  Alan M 1  (talk) &#93;— 22:49, 14 June 2013 (UTC)


 * (edit)Actually, reading the statement, it's entirely correct. It simply claims that "limit" is usually abbreviated "lim". This being English Wikipedia, there's no rule that you must mention what the word translates to in Latin, Greek, or Swahili, nor the etymology of it or its abbreviations. The sentence does not imply otherwise. —&#91;  Alan M 1  (talk) &#93;— 22:55, 14 June 2013 (UTC)

Inconsistent graphic?
At, the prose discusses a single scenario, and the right side of the graphic purporting to show it almost shows a zoomed-out view of the left side, but not quite. If the two sides are meant to represent the same thing, the left side needs the vertical line intersection with the x-axis at c - δ to be labeled "S". On the right side, f(x) needs to be equal to L + ε at x = c + δ (i.e. the second hump needs to be above the green-highlighted area). —&#91;  Alan M 1  (talk) &#93;— 23:17, 14 June 2013 (UTC)

Assessment comment
Substituted at 15:16, 1 May 2016 (UTC)

Lay Access to Mathematics
Just a quick comment. I would like to see pretty much ALL of our Math articles include something which occurs in this article. After a formula, let's always include a sentence in English explaining how the Math characters are read or would sound if spoken. For ex: from this article ... "the limit of f of n as n approaches c equals L". This kind of clarification is extremely helpful to Lay People and to less learned Mathematicians who are teaching themselves.

I believe the consistent inclusion will greatly improve any article containing Math symbols, and will not overly vex learned mathematicians who can simple skim past it. Thanks for the great articles. They are very much appreciated. — Preceding unsigned comment added by 97.125.84.64 (talk) 00:17, 20 February 2015 (UTC)

Copy of removed paragraph
Removed this:


 * ====A Brief Note Regarding Division by Zero====

In general, but not in all cases, should u directly substitute c for x (into f(x)) and obtain an illegal fraction with division by zero, check to see whether the numerator equals zero. In cases where such substitution results in 0 / 0, a limit probably exists; in other cases (such as 17 / 0) a limit is less likely. For instance; if f(x) = x&sup3; + 1 / x - 1; then, if one substitutes 1 for x, one will obtain 2 / 0; the limit of f(x) (as x approaches 1) does not exist.

I can't be bothered to do the graph offhand, but there will be a limit: either + or - inf. User:Tarquin — Preceding unsigned comment added by Tarquin (talk • contribs) 07:55, 8 June 2003 (UTC)

oops Pizza Puzzle — Preceding unsigned comment added by Pizza Puzzle (talk • contribs) 15:01, 8 June 2003 (UTC)


 * Plus and minus infinity are not limits according to the definition in the article. Please make sure that you have some understanding of the article before you go removing bits. -- Oliver P. 15:42, 8 June 2003 (UTC)

I'm not aware that infinity is a limit; because, infinity is not a real number and my understanding is that limits must be real numbers. Pizza Puzzle — Preceding unsigned comment added by Pizza Puzzle (talk • contribs) 15:59, 8 June 2003 (UTC)


 * Yes, that's what I just said. I said it in reply to your statement that "there will be a limit: either + or - inf". If you have changed your mind, and are retracting your previous statement, please replace what you removed from the article. -- Oliver P. 16:02, 8 June 2003 (UTC)

No sir! I did not state that there will be a limit either + or - inf. The user who does not sign his messages stated that. I have added: which I believe is what u are referring to above. There is now the question of, if the above user was wrong, does that mean I can reinsert my text: or would that be a hostile revert? He had initially removed the entire paragraph, which I put most of it back in, but I didnt put the final line back since there was a debate of sorts regarding it. — Preceding unsigned comment added by Pizza Puzzle (talk • contribs) 16:09, 8 June 2003 (UTC)
 * the behavior of a function as its arguments get "close" to some point (or attempts to get close to infinity),
 * For instance; if f(x) = x&sup3; + 1 / x - 1; then, if one substitutes 1 for x, one will obtain 2 / 0; the limit of f(x) (as x approaches 1) does not exist.

Infinite limit

 * As x approaches 0, F(x) = 1 / x² is not approaching a limit as it is unbounded; a function which approaches infinity is not approaching a limit. Note that as x approaches infinity, F(x) = 1 / x² does approach a limit of 0.

Pizza Puzzle — Preceding unsigned comment added by Pizza Puzzle (talk • contribs) 16:12, 8 June 2003 (UTC)

Oh, I see! In that case, I apologise unreservedly for having accused you. I'll blame Tarquin for my error, though, since he was the phantom non-signer. ;) There is a problem in that there are different ways of defining what a limit is. I'll give the article some thought, and come back to it later. I wouldn't object to you putting that example back in, although you should leave out the idea of substitution; a limit only depends on the behaviour as you appraoch the point, not at the point itself. -- Oliver P. 16:15, 8 June 2003 (UTC)

The subsitution point is, IF you substitute, and you get division by zero, if you get 0 / 0, then there is probably a limit, otherwise there probably isn't. Pizza Puzzle — Preceding unsigned comment added by Pizza Puzzle (talk • contribs) 16:17, 8 June 2003 (UTC)

Oh, I'll think about it later. I should be doing work... -- Oliver P. 16:29, 8 June 2003 (UTC)

Now here, this text says (in so many words): "The limit, L of f(x), as f(x) increases (or decreases) without bound is an infinite limit. Be sure that you see that the equal sign in "L = infinity" does not mean that the limit exists. Rather, this tells you that the limit fails to exist by being boundless."

It would appear, that it is correct to refer to "infinite limits" but one should understand that an "infinite limit" is not a limit. See also: "unbounded limit" Pizza Puzzle — Preceding unsigned comment added by Pizza Puzzle (talk • contribs) 19:05, 8 June 2003 (UTC)

Would it be too much to expect User: AxelBoldt to explain some of his more "major" changes? It appears that a great deal of information was deleted. If he had a problem with it, it would have been more appropriate to discuss it or improve it; rather than merely deleting it. Pizza Puzzle — Preceding unsigned comment added by Pizza Puzzle (talk • contribs) 20:48, 18 June 2003 (UTC)

Too many subsections before the formal definition. I don't think an encyclopedia article should go that way. I will try to rewrite this later. Wshun — Preceding unsigned comment added by 142.179.20.95 (talk) 05:13, 1 August 2003 (UTC)

I see limits in this way. If the function is continous for all R then at the limit the function will have a definte value. It doesn't matter if you are trying to find the limit at + or - infinity, or the limit of a function as it approaches a certain value c. In both cases you are dealing with an infinte number of values. If there was no definte value at the limit then limits would'nt be of much use in calculus. — Preceding unsigned comment added by 81.152.39.231 (talk) 18:09, 23 April 2004 (UTC)