3 ms·
Why can’t you asume S(2)? Is it not included in the inductive hypothesis S(k)?
by solids 6y ago
Why 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 :-)