Talk:Limit (mathematics)
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| Mathematics grading: | B Class | High Importance | Field: Analysis | ||
| Need to expand sections on "Topological net and "Category theory"; needs more prose to accompany equations, plus history and more on applications. Tompw 16:22, 7 October 2006 (UTC) | |||||
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)
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) = x³ + 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
oops Pizza Puzzle
- 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 Jun 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
- 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 Jun 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:
- the behavior of a function as its arguments get "close" to some point (or attempts to get close to infinity),
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:
- For instance; if f(x) = x³ + 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.
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.
Contents |
[edit] ACHTUNG SPITFEUER
- 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.
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 Jun 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
Oh, I'll think about it later. I should be doing work... -- Oliver P. 16:29 8 Jun 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
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
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
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.
[edit] 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)
[edit] Oscillating Limits
Consider Grandi's alternating series
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)
[edit] 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. --Nickvkalker 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 Nickvkalker added a vandalism warning to the article itself. Needless to say, that was a bad idea. Melchoir 03:15, 18 July 2006 (UTC)
[edit] 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)
[edit] 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)
[edit] 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)
[edit] 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)
[edit] 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)
