Question: Let b 2 be an integer. Define a representation of a real number in [0,1] in terms of base b rather than base 10 and

Let b 2 be an integer. Define a representation of a real number in [0,1] in terms of base b rather than base 10 and prove Proposition 1.5.1 . for base b.

Proposition 1.5.1 :

(i) Every infinite sequence of digits 0.d1d2d3 ... represents a unique real number x [0,1], and Dn x Dn + 1/10^n for all n N.

(ii) For every x (0,1] there exists an infinite sequence of digits 0.d1d2d3 ... that represents x. There exists a unique representation such that Dn < x Dn + 1/10^n for all n N.

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