5. (10%) Here is an incorrect use of induction to claim that all natural numbers

Question

5. (10%) Here is an incorrect use of induction to claim that all natural numbers are equal. Expose the fallacy ·Consider the following property P of natural numbers n: all natural numbers n are equal. We show by induction that P is true of all n. Basis. P is true vacuously ofn -0, since the only natural number 0 is 0 itself. Step. Suppose P is true of n-k. To show that P is true of n-k + 1, suppose that x, y k+1. Then the two numbers x-1 and y-1 are identical, by IH, since they are A. Therefore x y

Explanation / Answer

Fallacy is Basis step: n=0 is a natural number.

It is false step as n=0 is not a natural number

We should take n=1 in basis step

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