Bounded sequence doubt

  • Thread starter Ryuzaki
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  • #1
Ryuzaki
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Thomas-Finney defines a bounded sequence as follows: -

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

This is equivalent to saying -M ≤ an ≤ 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 an 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 ≤ an ≤ M , for some N belonging to real numbers?

Thanks.
 

Answers and Replies

  • #2
jbriggs444
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But what if all values of an 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).
 

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