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EXAMPLE 4.6. Let X = Q, the rational numbers with distance between any two rational numbers x and y, be defined as d(x, y) = |x − y\. One can easily make up Cauchy sequences of rational numbers that converge to irrational numbers. Hence this space is not complete.

EXAMPLE 4.6. Let X = Q, the rational numbers with distance between any two rational numbers x and y, be defined as d(x, y) = |x − y\. One can easily make up Cauchy sequences of rational numbers that converge to irrational numbers. Hence this space is not complete.

Advanced Engineering Mathematics
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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EXAMPLE 4.6. Let X = Q, the rational numbers with distance between any two rational numbers x and y, be defined as d(x, y) = |x − y\. One can easily make up Cauchy sequences of rational numbers that converge to irrational numbers. Hence this space is not complete.
Transcribed Image Text:EXAMPLE 4.6. Let X = Q, the rational numbers with distance between any two rational numbers x and y, be defined as d(x, y) = |x − y\. One can easily make up Cauchy sequences of rational numbers that converge to irrational numbers. Hence this space is not complete.
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