Thomas-Finney defines a bounded sequence as follows: -(adsbygoogle = window.adsbygoogle || []).push({});

A sequenceais said to be bounded if there exists a real number_{n}Msuch 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 ofalies 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Bounded sequence doubt

**Physics Forums | Science Articles, Homework Help, Discussion**