- #1
jack476
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Assuming you've sufficiently proven your inductive basis, can you complete a proof by induction in the following manner:
Make the inductive hypothesis, assume P(n) is true for some n. Assume P(n+1) is not true. If it follows from the assumption that P(n+1) is false that P(n) must also therefore be false, contradicting the inductive hypothesis, does this mean P(n) must imply P(n+1)?
Make the inductive hypothesis, assume P(n) is true for some n. Assume P(n+1) is not true. If it follows from the assumption that P(n+1) is false that P(n) must also therefore be false, contradicting the inductive hypothesis, does this mean P(n) must imply P(n+1)?