- #1
Nusc
- 760
- 2
Let S be an infinite and bounded subset of R. Thus S has a point of accumulation.
Proof: Let T be the set of reals such that for every t E T there are infinitely many elements of S larger than t. Let M be such that -M<S0<M for all S0 E S.
The set T is nonempty and bounded and hence it has a supremum say A.
Proof of claim: A is an accumulation point of S.
Can someone please help me with the proof of the claim or give it to me rather? Never did I expect such a course that demanded so much memorization.
Thanks
Proof: Let T be the set of reals such that for every t E T there are infinitely many elements of S larger than t. Let M be such that -M<S0<M for all S0 E S.
The set T is nonempty and bounded and hence it has a supremum say A.
Proof of claim: A is an accumulation point of S.
Can someone please help me with the proof of the claim or give it to me rather? Never did I expect such a course that demanded so much memorization.
Thanks