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:Â Â 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
