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Fix a prime number p. For x EQ - {0}, write x = p" () where a, b € Z, a and b are not divisible by p. Define For x, y E Q, define Show that (Q, d) is a metric | x |p == space. = { p", 0, if x #0 if x = 0 d(x, y) = |xy|p

Fix a prime number p. For x EQ - {0}, write x = p" () where a, b € Z, a and b are not divisible by p. Define For x, y E Q, define Show that (Q, d) is a metric | x |p == space. = { p", 0, if x #0 if x = 0 d(x, y) = |xy|p

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Fix a prime number p. For x = Q = {0}, write x = = p" () where a, b € Z, a and b are not divisible by p. Define For x, y EQ, define |x|p == Show that (Q, d) is a metric space. = {} 0, p-n, if x # 0 if x = 0 d(x, y) = |x — yp
Transcribed Image Text:1. Fix a prime number p. For x = Q = {0}, write x = = p" () where a, b € Z, a and b are not divisible by p. Define For x, y EQ, define |x|p == Show that (Q, d) is a metric space. = {} 0, p-n, if x # 0 if x = 0 d(x, y) = |x — yp
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