Bounded Sequence: Thomas-Finney Definition Explained

[Ryuzaki]

Thomas-Finney defines a bounded sequence as follows: -

A sequence a_n is said to be bounded if there exists a real number M such that |a_n| ≤ M for all n belonging to natural numbers.

This is equivalent to saying -M ≤ a_n ≤ M

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 a_n lies between, say -3 and 1, i.e in the interval (-3,1)? Is it still bounded?

By the above definition it isn't. Essentially what I'm asking is whether the definition can be N ≤ a_n ≤ M , for some N belonging to real numbers?

Thanks.

 

[jbriggs444]

But what if all values of a_n lies between, say -3 and 1, i.e in the interval (-3,1)? Is it still bounded?

If all the values lie in the interval (-3,1) then they also lie in the interval (-3,3).