Unformatted text preview: a and b are integers, and then partition [ a, b ) into the disjoint union of halfopen intervals [ n, n +1), n = a, a +1 , . . . , b1. For at least one such n , the subinterval [ n, n + 1) contains inﬁnitely many terms x j (the precise meaning of which is, as usual, contains x j for inﬁnitely many positive integers j ). Let us ﬁx the smallest n ∈ { a, a + 1 , . . . , b1 } with the property just named. This will be the integer part of our decimal expansion n.d 1 d 2 d 3 . . . . We also set t = x j (0) for the smallest positive integer j (0) with x j (0) ∈ [ n, n + 1). (Note that such j (0) exist, in fact, there are inﬁnitely many of them.) Obviously, (3) now holds for j = 0. We now describe how to choose d j +1 and . ... further text in preparation...
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This note was uploaded on 11/08/2011 for the course MATH 601 taught by Professor Osu during the Fall '11 term at Cornell.
 Fall '11
 OSU
 Math

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