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Question: 16 the definition of distance 13 exercises the crucial step...

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1.6 The Definition of Distance 13 ExERCISES The crucial step in the proof that V2 is irrational is showing that m2 even implies m is even or, equivalently, that m odd implies m2 odd. It is worth taking a 1.5.1i Writing an arbitrary odd number m in the form 2q+ 1, for some integer q, You probably did some algebra like this in Exercise 1.2.3, but if not, here is 1.5.2/Show that the square of 2q+1 is in fact of the form 4s+1, and hence explain closer look at why this is true. show that m2 also has the form 2r + 1, which shows that m2 is also odd. your chance: why every integer square leaves remainder 0 or 1 on division by 4. 1.6 The Definition of Distance The numerical interpretation of irrationals gave each length a numerical measure and hence made it possible to give coordinates x, y to each point
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