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Copy of removed paragraph
- ====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.
- 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.
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. —[AlanM1(talk)]— 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. —[AlanM1(talk)]— 22:55, 14 June 2013 (UTC)
At Limit (mathematics) § Limit of a function, 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). —[AlanM1(talk)]— 23:17, 14 June 2013 (UTC)