Asked by Lucy
Hello. I want make sure im doing right step.
Prove the supremum of the set A={2-1/n: n in natural number} is 3.
My answer
Proof: lets prove supA=2
Then 2 is an upper bound of A.
Let S'<2, then S' is not upper bound.
There exists x in A such that x> S'
Then 0<2-S'
There exists n in natural number such that 0<1/n <2-S'
Therefore supA=2. QED.
Prove the supremum of the set A={2-1/n: n in natural number} is 3.
My answer
Proof: lets prove supA=2
Then 2 is an upper bound of A.
Let S'<2, then S' is not upper bound.
There exists x in A such that x> S'
Then 0<2-S'
There exists n in natural number such that 0<1/n <2-S'
Therefore supA=2. QED.
Answers
Answered by
Lucy
I mean prove the supremum of the set {2-1/n: n in N} is 2
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