
Bogus Induction
A Bogus Proof Theorem: All horses are the same color. Proof: (by induction on n) Induction hypothesis: P(n) ::= any set of n horses are the same color
A Bogus Proof Theorem: All horses are the same color. Proof: (by induction on n) Induction hypothesis: P(n) ::= any set of n horses are the same color Base case (n=1): horse is same color as itself!
(Inductive case): Assume n horses have the same color. Prove that any n+1 horses have the same color. A Bogus Proof
A Bogus Proof (Inductive case): Assume n horses have the same color. Prove that any n+1 horses have the same color.
A Bogus Proof (Inductive case): Assume n horses have the same color. Prove that any n+1 horses have the same color.
so set of n+1 have the same color! 1st and last same color as the middle ones A Bogus Proof QED ?!?
What’s wrong? Proof that P(n) → P(n+1) is wrong if n = 1 , because there are no “middle” horses! A Bogus Proof
Proof that P(n) → P(n+1) is wrong if n = 1 , because there are no “middle” horses! What’s wrong? A Bogus Proof mislead by ellipsis
Proof that P(n) → P(n+1) is wrong if n = 1 (But proof works for all n ≠ 1) , because there are no “middle” horses! What’s wrong? A Bogus Proof
URL: 
No comments posted yet
Comments