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As far as I know there are five kinds of vote

  • $+2$ for an edit
  • $-2$ for a downvote
  • $+10$ for an answer
  • $+15$ for an accepted answer
  • $+5$ for a question

Suppose that this is true. Can a MSE reputation take any positive integer value? How do you prove it?

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You forgot the +100 association bonus. Furthermore, there is the +200 reputation cap which may cause you to get only a part of some reputation (edit, answer, accepted answer) score when you hit that cap. – azimut Nov 4 '13 at 10:52
if one downvotes something one gets -1. – miracle173 Nov 4 '13 at 13:38
No. The universe will experience a heat death, so time is finite, and hence the total number of possible MSE posts is finite. Your reputation cannot be any positive integer. – nayrb Jun 5 '14 at 18:03
up vote 12 down vote accepted

Yes. Just note that one upvote on a question, and then two downvotes equal $1$ point in reputation.

(Also note that $+2$ for edits only hold below a certain limit; and you can lose a point by downvoting an answer.)

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Yes, since $\gcd(2,15)=1.$ Then use that $15-7(2)=1=15+7(-2)$ Multiply this by any $n$ to get $n$ points.

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