Recent content by mmilton

Homework Statement How can I show that the sup(S)=lim{Xn} and the inf(S)=lim{Yn} as n goes to infinity for both of those limits? We are assuming S is a nonempty bounded set that is a subset of the Real numbers. Also, {Xn} and {Yn} are monotone sequences that belong to the the set S...

Homework Statement Is the sequence {n/(n^2+1)} convergent, and if so, what is it's limit?Homework Equations The Attempt at a Solution I believe it does converge because the higher power is in the denominator, so thus, it's limit is 0. Any help or hints on if I'm headed in the right direction...

Thank you Ray! Great explanation. I understand it now.

Yes, it is a sequence. I only used "sum" because I was initially confused and was asking whether I could use AST on the sequence.

It is a sequence. So, does that preclude using the alternating series test (i.e. is that only used on series)?

Homework Statement Is the sequence {((-1)^n)/2n} convergent? If so, what is the limit? Homework Equations The Attempt at a Solution I'm thinking that it is convergent by the alternating series test, but I am not certain. The limit part I'm not sure how to go about it. Is it...

Homework Statement Is the sequence {n} convergent? Homework Equations The Attempt at a Solution I believe that it is not convergent. I'm thinking that I could show this by a Proof by contradiction, but I am not certain. Am I going down the right route? Thanks.

Homework Statement Let f: A --> B be an injection and suppose that the set A is countably infinite; how can I prove that there is an injection from B to A if and only if B is countably infinite? Also, if we would suppose that A is uncountable, can B be countable? Homework Equations...