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2.1 Let B be the set of all bounded sequences of real numbers and define the function d : B × B → R by d(x, y): = sup |an – Yn . Show that (B, d) is a metric space. 2 2 Civon (IDn A with 1. Dn P dofinod bu

2.1 Let B be the set of all bounded sequences of real numbers and define the function d : B × B → R by d(x, y): = sup |an – Yn . Show that (B, d) is a metric space. 2 2 Civon (IDn A with 1. Dn P dofinod bu

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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metric space

2.1 Let B be the set of all bounded sequences of real numbers and define the function d : B × B → R by d(x, y): = sup |an – Yn|. Show that (B, d) is a metric space. 2.2 Given (R", d) with d : R" × R" → R defined by d(x, y) 2(*k – Yk)². k=1
Transcribed Image Text:2.1 Let B be the set of all bounded sequences of real numbers and define the function d : B × B → R by d(x, y): = sup |an – Yn|. Show that (B, d) is a metric space. 2.2 Given (R", d) with d : R" × R" → R defined by d(x, y) 2(*k – Yk)². k=1
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