Answered: d (n, m): = 0 si n = m si n‡m 5-c(n-m)

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d (n, m): = 0 si n = m si n‡m 5-c(n-m)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 18E

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Question

Let c(n) be the largest power of 5 that divides n ∈ Z \ {0}, for example c(5)=1, c(15)=3 , c(250)=50 , c(7) = 0, etc. The function
d (n, m) = 0 if n = m and d(n, m) = 5^−c(n−m) if n ≠ m
defines a metric on Z. Who is B(0, 1)?
Who is B(0, 1)?
Prove that the sequence 10, 1100, 111000, 11110000, ... converges to 0 in (Z, d).