- #1
retspool
- 36
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Analysis , sequences, limits, supremum explanation needed :(
So i have a question and the answer as well, but i will need some explanation.
here is the Question
Let S be a bounded nonempty subset of R and suppose supS ∉S . Prove that there is a
nondecreasing sequence (Sn) of points in S such that lim Sn =SupS .
Answer Proof
Since supS ∉ S , there exist Sn ∈ S for all n ∈N such that Sn > S - 1/n
.
Hence limSn = supS and (Sn) is a nondecreasing sequence.
So i have a question and the answer as well, but i will need some explanation.
here is the Question
Let S be a bounded nonempty subset of R and suppose supS ∉S . Prove that there is a
nondecreasing sequence (Sn) of points in S such that lim Sn =SupS .
Answer Proof
Since supS ∉ S , there exist Sn ∈ S for all n ∈N such that Sn > S - 1/n
.
Hence limSn = supS and (Sn) is a nondecreasing sequence.
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