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# Bounded Functions watch

1. How would you go about proving that,

with

Is bounded? I tried with m >= s >= M but don't get very far...
2. Is s > 0? Is s < 1?
3. (Original post by DFranklin)
Is s > 0? Is s < 1?
The question doesn't say, just that s is in R and n = 1, 2, 3, ..
4. (Original post by Blue7195)
The question doesn't say, just that s is in R and n = 1, 2, 3, ..

You may need to do a tiny bit of algebra...
5. (Original post by DFranklin)

You may need to do a tiny bit of algebra...
Oh sorry, I worked out the infimum and supremum to be 0 and 1 so yeah. Is that all you need to show?
6. (Original post by Blue7195)
..
A sequence a_n is bounded if we can find constants m, M s.t. m <= a_n <= M for all n.

Without wanting to snark, the first thing you need to do when answering a question is making sure you understand the terms being used. Finding the sup, inf is not necessary here.
7. (Original post by DFranklin)
A sequence a_n is bounded if we can find constants m, M s.t. m <= a_n <= M for all n.

Without wanting to snark, the first thing you need to do when answering a question is making sure you understand the terms being used. Finding the sup, inf is not necessary here.
Ah okay thanks a lot!

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Updated: January 21, 2015
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