Decide if the following are true or false and provide a proof or counterexample:

Suppose that x{n} --> L.

a) For all e > 0, there exists a natural number n such that |x{n+1} − x{n}| < e

b) There exists a natural number n such that for all e > 0, |x{n+1} − x{n}| < e

c) There exists e > 0 such that for all natural numbers n, |x{n+1} − x{n}| < e

d) For all natural numbers n, there exists e > 0 such that |x{n+1} − x{n}| < e

e stands for epsilon, which is a very small number. { } are subscripts.