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 Nov 23 comment Is mathematics the only language that is not subject of interpretation? @Derfder: please, don't think you understand string theory if you don't even get the uncertainty principle. Nov 23 revised Is mathematics the only language that is not subject of interpretation? deleted 1 characters in body Nov 23 comment Is mathematics the only language that is not subject of interpretation? @Derfder: i don't really get your comment, what are you trying to say? Nov 23 answered Is mathematics the only language that is not subject of interpretation? Nov 23 comment Not understanding modulo i agree with that very first equation, but for a non-mathematician it might seem unnatural, and of course it is of huge importance in ring theory so some explanation could be useful Nov 22 comment How many possible choices are there? For the existence part, start from any vertex $n$, and choose $i$ such that the partial sum of the integers from vertex $n$ through $i$ is minimal. Now, for any $k$, starting from $i+1$ will work. Nov 19 comment About a Dirichlet problem I think the answer is yes, but I'm not sure why. Nov 18 comment Why does $16^{1/3} = 2^{4/3}$ I wish SE would have a "like" option alongside the upvote. Nov 18 comment Axiomatically define a function that can solve otherwise impossible differential equations, like $i$ solves otherwise impossible polynomial equations @J.M.: it sure is, it has a term $0\cdot\frac{df}{dx}$ Nov 18 comment Axiomatically define a function that can solve otherwise impossible differential equations, like $i$ solves otherwise impossible polynomial equations I think every mathematician would agree we start looking for solutions in the space of continuous functions anyway - heck, we define many functions in terms of differential equations! Only the last paragraph actually relates to the question, and it is not very scientific... Nov 18 comment Axiomatically define a function that can solve otherwise impossible differential equations, like $i$ solves otherwise impossible polynomial equations @J.M.: I don't think the term "closed form" is more helpful than my explanation, but yes, that would be the right term :) Nov 18 comment Axiomatically define a function that can solve otherwise impossible differential equations, like $i$ solves otherwise impossible polynomial equations @SeyhmusGüngören: no, not all differential equations can be solved, for example the equation $f(x)=f(x)+1$. However, such unsolvable equations are not physically interesting. I do not know if there is some abstract branch which investigates these equations nonetheless. Nov 18 comment Axiomatically define a function that can solve otherwise impossible differential equations, like $i$ solves otherwise impossible polynomial equations @SeyhmusGüngören: I think it is important to note that many differential equations /are/ solvable in the sense that there exists a function satisfying it, it's just that we do not have an expression for that function in terms of the "ordinary" notation. Nov 18 comment Axiomatically define a function that can solve otherwise impossible differential equations, like $i$ solves otherwise impossible polynomial equations @J.M.: Many constant polynomials have no solution. Nov 18 comment Axiomatically define a function that can solve otherwise impossible differential equations, like $i$ solves otherwise impossible polynomial equations @SeyhmusGüngören, is your question whether every equation which is not solvable in the real numbers, solvable in complex numbers? Nov 11 comment troubles proving every subset of a finite set is finite with naive set theory +1 for clear question statement. Nov 10 comment topology-Quotient topology,quotient space it would be very helpful if you could provide a more helpful title, and the actual example, because I don't have the book. Nov 8 comment How to take this limit Use boundedness of sin. Nov 6 comment Finding an asymptotic for the sum $\sum_{p\leq x}p^m$ @JoseGarcia: see below for a somewhat-proof. Nov 6 revised Finding an asymptotic for the sum $\sum_{p\leq x}p^m$ added 570 characters in body