I read that the Dirichlet function (1 if Rational, 0 else) can be written as: What is the proof of that? Are those limits commutative? Is there any other closed formula for Dirichlet function? (With ...
Let a function exist such that $f(a+b)=f(a)+f(b)$. We have already shown that for any integer n, $f(nx)=n f(x)$. Now we must show that for any rational number $n/m$, $f(n/m)=n/m f(1)$. The problem is ...
I have found next formula of counting all rational numbers (or integer pairs, from which rational numbers can be builded): $N(i,j) = ((i - j - 1)(i - j) - 2j - 1)(1 + j / |j|)/2 + ((i + j - 1)(i + j) ...