We may use the fact that if , then both and .
Let l be an element of R, c be an element of R, c>0. Show that the following two statements are equivalent:
a)for every epsilon>0 there exists N that's an element of the natural numbers for every n>or=N such that |xn-l|< epsilon
b)for every epsilon>0 there exists N that's an element of the natural numbers for every n>or=N such that |xn-l|< (c)epsilon
I came across this problem in my textbook while studying, but can't figure out how to approach it. Any help would be great!