5 ms·
Not exactly, it was saying that you assumed S(2) implicitly which is wrong.
by cheez 6y ago
Not exactly, it was saying that you assumed S(2) implicitly which is wrong.
- cf-d-ycom 6y agoYeh, that makes more sense.
- solids 6y agoWhy can’t you asume S(2)? Is it not included in the inductive hypothesis S(k)?
- cf-d-ycom 6y agoSo the base case that they prove is S(1). And the inductive step is to show: S(1) ->(implies) S(2) -> S(3) -> S(4) -> .... Or to write it more succinctly, that S(n) -> S(n + 1) assuming S(n) is true. In this particular problem, the proof that is provided can be used to show S(2) -> S(3), that S(3) -> S(4), etc... are valid and true. However, the proof could NOT be applied to show that S(1) -> S(2). So whilst you CAN assume S(2) is true in a proof, the whole inductive chain needs to be attached to a valid base case.
- cheez 6y agoThe page gives a better explanation than I could :-)