The Pythagoreans and Irrationality
Two lengths a and b are commensurable if there are positive integers p and q such that a/b = p/q. When the Pythagoreans claimed that all things are numbers, they meant to imply that all pairs of lengths are commensurable. For the Pythagoreans, ‘number’ meant ‘rational number’.
KeywordsRational Number Integer Solution Diophantine Equation Concise History Unit Fraction
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