- #1
Ryuzaki
- 46
- 0
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.
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.