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

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- Nov 15th 2013, 04:47 AMdavidciprutDefinition of limits of a sequence
Can someone explain me what n, N represent and why N<n? Thank you.

- Nov 15th 2013, 05:01 AMPlatoRe: Definition of limits of a sequence
If $\displaystyle (x_n)\to l$ means that

**almost all**of the terms of $\displaystyle x(_n)$ are close to the number $\displaystyle l$.

**Almost all means all but a finite collection of the terms.**

If $\displaystyle N\in\mathbb{Z}^+$ then the set $\displaystyle \{1,2,\cdots N\}$ is a finite set and the set $\displaystyle \{n:n>N\}$ is an infinite set.

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