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Limit may or may not exist but can it also be undefined? Am I right that the limit will be undefined (not D.N.E) when function is not defined at the neighbourhood of that point where limit is being evaluated?

Mathematics
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  • IMO the two are the same. We may say that the operation of "computing the limit" of e.g. $f(x)$ is undefined, i.e. it outputs no result, exactly because there is no number that satisfies the definition: "limit of $f(x)$ at..." – Mauro ALLEGRANZA Oct 26 '20 at 11:28
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    If I understand well, you want to make a distinction between "the limit does not exists because the function is not defined in a neighbourhood of the point" and "the limit does not exists even if the function is defined in a neighbourhood of the point" ? Well, if you want, make a distinction :) But I don't think there are distinct words to describe these two situations. – TheSilverDoe Oct 26 '20 at 11:33
  • Is there any difference b/w saying limit does not exist or limit is undefined?But i think there is difference. – Mathematics Oct 26 '20 at 12:06
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    You should precisely explain which type of limit you are considering. It seems that you consider functions - but what are domain and range? $\mathbb R$? – Paul Frost Oct 26 '20 at 12:27
  • Can limit be undefined? Is there any difference between undefined and does not exist in the context of limit? – Mathematics Oct 26 '20 at 13:25
  • Why are you repeating the question without even answering the given comments ? – TheSilverDoe Oct 26 '20 at 14:30
  • You didn't tell me the answer of my question.My question is "Is there any difference between undefined and D.N.E?" Can limit be undefined? – Mathematics Oct 27 '20 at 02:54

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