Definition of limits of a sequence

• Nov 15th 2013, 04:47 AM
davidciprut
Definition of limits of a sequence
Can someone explain me what n, N represent and why N<n? Thank you.
• Nov 15th 2013, 05:01 AM
Plato
Re: Definition of limits of a sequence
Quote:

Originally Posted by davidciprut
Can someone explain me what n, N represent and why N<n? Thank you.

If $(x_n)\to l$ means that almost all of the terms of $x(_n)$ are close to the number $l$.

Almost all means all but a finite collection of the terms.
If $N\in\mathbb{Z}^+$ then the set $\{1,2,\cdots N\}$ is a finite set and the set $\{n:n>N\}$ is an infinite set.

So in the that definition to say $n>N$ means that infinite set is almost all of the terms.