bogus-induction

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Slide 1

Bogus Induction

Slide 2

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

Slide 3

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!

Slide 4

(Inductive case): Assume n horses have the same color. Prove that any n+1 horses have the same color. A Bogus Proof

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A Bogus Proof (Inductive case): Assume n horses have the same color. Prove that any n+1 horses have the same color.

Slide 6

A Bogus Proof (Inductive case): Assume n horses have the same color. Prove that any n+1 horses have the same color.

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so set of n+1 have the same color! 1st and last same color as the middle ones A Bogus Proof QED ?!?

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What’s wrong? Proof that P(n) → P(n+1) is wrong if n = 1 , because there are no “middle” horses! A Bogus Proof

Slide 9

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

Slide 10

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

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