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August 19th, 2006

Reasons for Irrational Numbers

Posted to mathematics where a thorough debate followed the x-posting to philosophy's discussion:

A demonstration of Pythagras' Theorem followed by Hippasus's Proof, the points I make being from my concluding questions: Seeing any need for √2, the most interesting question is how does mathematics envelop new numbers?  After answering that, what extrensic reason is there for enveloping √2 into a number system?  Hippasus' indirect proof merely demonstrated, contrary to our intuition, that √2 cannot be expressed as a rational number p/q; it says nothing about what should replace the assumption from line 8.  And I am not satisifed that we have solved this problem for reasons other than the ideal consistency of the real numbers.