Definition of limit: $\forall n>N$ or $\forall n \geq N$?

Question

My question is about the definition of limit.

Definition: The number $a$ is said to be the limit of the sequence $\{x_n\}$ if $\forall \epsilon > 0$, $\exists N \in \mathbb{N}$ such that $\forall n > N$, we have $$|x_n - a| < \epsilon.$$

This definition is in the book "The fundamentals of Mathematical Analysis - Fikhtengol'ts". But in "Principles of Mathematical Analysis - Walter Rudin", he uses the condition $n \geq N$. Is there any difference in the definition of limit when we use the conditions $n>N$ and $n \geq N$?

Answer 1

No, since $n>N\iff n\geqslant N+1$.

Answer 2

No. There are no differences ! Try a proof !

Answer 3

No, because both of them means the same: the inequality $|x_n-a|<\epsilon$ holds true for every natural number except finitely many.