Comment on Rationality Quotes September 2012

Thu, 06 Sep 2012 07:53:26 GMT

Looking over my post again, after a good night's sleep, I see that it wasn't as coherent as it appeared to me yesterday. Let me see if I can put my point a little more clearly.

The paragraph centers its claim of the irrationality of √2 on the idea that p² contains exactly twice as many powers of 2 as p does. But that is only true because √2 is irrational, making the demonstration a circular proof.

Consider. If √2 were rational, in the form of z/y for some coprime integers z and y, then it would be easy to find an integer that is not itself an integer power of 2, but whose square is an integer power of 2; z would be such a number.

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