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al numbers R\Q is dense in R.

al numbers R\Q is dense in R.

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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A subset E of a metric space (S, d) is dense in S if for every point s ES and every e>0 there is a point TEE so that d(r, s) <e. Prove that the set of irrational numbers R\Q is dense in R.
Transcribed Image Text:A subset E of a metric space (S, d) is dense in S if for every point s ES and every e>0 there is a point TEE so that d(r, s) <e. Prove that the set of irrational numbers R\Q is dense in R.
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