Let de(x, y) := |x — y|, d₁(x,y) := for x,y E R. Show that (a) d₁ is a metric on R; (b) dẼ and d₁ are not equivalent. |x - y| 1 + x − y|

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2. Let
de(x, y) = |x — y|, d₁(x, y) =
for x, y E R. Show that
(a) d₁ is a metric on R;
(b) de and d₁ are not equivalent.
|x - y|
1 + x - y
Transcribed Image Text:2. Let de(x, y) = |x — y|, d₁(x, y) = for x, y E R. Show that (a) d₁ is a metric on R; (b) de and d₁ are not equivalent. |x - y| 1 + x - y
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