This is probably really easy, but i am really rusty and i want to really understand. I am trying to understand why [tex] log(n) < n^a [/tex] For all n,a>0. I am really having a hard time to get an intuition over this, of course if i let a >= 1 then its obvious, but how do i know if there is not some extremely small epsilon that breaks the inequality. I understand maybe i should use that in a proof but i am kinda stuck. Also this is not really directly related but a thought i had, is there a name for functions that has the property that if x < y then g(x) < g(y), i'm curious.