Hi I am having problems with a couple of questions on my current assignment. I assume both questions are relating to the delta/epsilon proof of limits, which was given alongside the assignment.
Lets f1(x) = x, f2(x) = 2x, ..., fn(x) = nx. Then lim[x->0] fn(x)=0 for each n. Does there exist a positive number delta such that for every positive integer n we have absolute(fn(x)-0) <1 whenever 0< absolute(x-0) < delta
Let f(x) = 1 if x is rational, 0 if x is irrational. Show that lim[x->0] f(x) does not exist.