Is the the intersection of a finite number of compact sets is compact? If not please give a counter example to demonstrate this is not true. I said that this is true because the intersection of finite number of compact sets are closed. Which therefore means that it will be bounded because the in...

I will show that, for every $\sigma$ other than the identity, there is something in $A_n$ that does not commute with it. Since $\sigma$ is not the identity, $\sigma$ maps some element $a$ into $b$ with $a\ne b$. Choose $c$ and $d$ not equal to $a$ and $b$ (which I can do because $n>3$). Then I c...

Consider the expression $$\frac{\int_0^1 Ei(x)^5 ln(x) dx}{\int_0^1 Ei(x)^3 ln(x) dx} $$ A) Can we rewrite this with a single integral sign ? B) Do we have a closed form for this expression in terms of hypergeometric functions ? C) Is there a closed form without hypergeometric functions for ...