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## Main Question or Discussion Point

Thomas-Finney defines a bounded sequence as follows: -

A sequence

This is equivalent to saying -M ≤ a

So, if all terms of a sequence lies between, say -1 and 1, i.e. in the interval (-1,1), then its bounded.

But what if all values of

By the above definition it isn't. Essentially what I'm asking is whether the definition can be N ≤

Thanks.

A sequence

**a**is said to be bounded if there exists a real number_{n}**M**such that |a_{n}| ≤ M for all n belonging to natural numbers.This is equivalent to saying -M ≤ a

_{n}≤ MSo, if all terms of a sequence lies between, say -1 and 1, i.e. in the interval (-1,1), then its bounded.

But what if all values of

**a**lies between, say -3 and 1, i.e in the interval (-3,1)? Is it still bounded?_{n}By the above definition it isn't. Essentially what I'm asking is whether the definition can be N ≤

**a**≤ M , for some N belonging to real numbers?_{n}Thanks.