a) Suppose that 0 < y < 1/10 n for some integer n > 0. Prove that
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a) Suppose that 0 < y < 1/10n for some integer n > 0. Prove that there is an integer 0 < w < 9 such that w/10n+1 < y < w/10n+1 + 1/10n+1.
b) Prove that given x ∊ [0, 1) there exist integers 0 < xk < 9 such that for all n ∊ N,
c) Prove that given x ∊ [0, 1) there exist integers 0 < Xk < 9, k ∊ N, such that
d) Using part c), prove that 0.5 = 0.4999... and 1 = 0.999....
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a Let E k Z k 0 and k 10 n1 y Since 10 n1 y 10 E 0 1 9 Hence w s...View the full answer
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