Re:All Horses Are the Same Color
by shkkmo on Saturday December 04, 2021 @09:12PM
(#29446164)
That isn't really a problem, just poorly worded (like a number of sentences in the article.) This is a pretty standard step of an inductive that should read more like: Given that n is some positive integer where every set of n horses has the same color...then you try to prove that holds true for n+1 as well.
The actual problem in that proof is setting up the proofs of the inductive rule. There is an implicit assumption/condition that n+1 >= 3 that is not acknowledged.
If you acknowledge that condition, then it becomes quite clear that you can only prove a base case for n = 1 and only prove an induction rule for n >= 2 .
The actual problem in that proof is setting up the proofs of the inductive rule. There is an implicit assumption/condition that n+1 >= 3 that is not acknowledged.
If you acknowledge that condition, then it becomes quite clear that you can only prove a base case for n = 1 and only prove an induction rule for n >= 2 .