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$S=\{ p \: \mathrm{if} \: n=p^r,r>1 \: \mathrm{and} \: 0 \: \mathrm{otherwise}\}$ Where $p$ is prime no. And $n$ is natural no. $S=\{0,0,0,2,0,0,0,2......\}$ my teacher says all $p$ and $0$ are limit point of set $S$ but according to def of limit point every neighborhood of limit point must contain infinite many point of set. so in general this set is $S=\{0,p\}$ where $p$ is prime no. so $0$ has no point in is nbd, as I thinks, so how it could be limit point of set $S$ but my teacher says their is infinite many zero in set so nbd of $0$ contains infinite many point of $S$ , so it is limit point Plz help bcz I am stuck between my thinking and my teacher bcz repeated elements in set can be taken as one

Ashu5765449
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  • I put dollar sign to change line but don't know where is gone – Ashu5765449 Sep 19 '16 at 05:44
  • I cleaned up your text with correct dollar signs and whatnot; I advise you to read a very brief tutorial on LaTeX or MathJax (as is used on MSE). –  Sep 19 '16 at 05:55
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    Are you sure $S$ is meant to be a set rather than a sequence? Your definition doesn't make much sense if $S$ is supposed to be a set. – Eric Wofsey Sep 19 '16 at 06:35
  • As you said sequence then a point come in mind that since given S is linked with natural no. So its a sequence so I think he must has taught about limit of sequence but not set. If I am thinking right then approve my thinking – Ashu5765449 Sep 19 '16 at 08:38

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