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Contradiction proof conception Prove: If A is true, then B is true Contradiction: If A is true,...

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Advance Math

Contradiction proof conception

Prove: If A is true, then B is true

Contradiction: If A is true, then B is false.

so we suppose B is false and follow the step to prove. At theend we get if A is true then B is true so contradict ourassumption

However,

Theorem: Let (xn) be a sequence in R. Let L∈R. If everysubsequence of (xn) has a further subsequence that converges to L,then (xn) converges to L.

Proof:  Assume, for contradiction, that (xn) doesn'tconverge to L

**my question is that at the end we will get no subsequence of(Xnk) converges to L (Xnk is a subsequence of Xn)****

why this is contradiction? This only shows theContrapositive side of the theorem

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