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Given the usual metric d: RXR>[0, 0) defined by d(x, y) = |x- yl, write the set B(x, r) in interval notation. I know the answer is (x – r, x + r) but wanted to know why.

Given the usual metric d: RXR>[0, 0) defined by d(x, y) = |x- yl, write the set B(x, r) in interval notation. I know the answer is (x – r, x + r) but wanted to know why.

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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Given the usual metric d: RX R→[0, 0) defined by d(x, y) =|x - yl, write the set B(x, r) in interval notation. I know the answer is (x – r, x + r) but wanted to know why.
Transcribed Image Text:Given the usual metric d: RX R→[0, 0) defined by d(x, y) =|x - yl, write the set B(x, r) in interval notation. I know the answer is (x – r, x + r) but wanted to know why.
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