Let SS be the set of numbers in X=[0,1]X=[0,1] that when expanded as a decimal form, the numbers are 4 or 7 only. The following are the problems. a), Is S countable ? b), Is it dense in XX ? c), Is it compact ? d), Is it perfect ?

Let SS be the set of numbers in X=[0,1]X=[0,1] that when expanded as a decimal form, the numbers are 4 or 7 only. The following are the problems. a), Is S countable ? b), Is it dense in XX ? c), Is it compact ? d), Is it perfect ?

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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Question

Let SS be the set of numbers in X=[0,1]X=[0,1] that when expanded as a decimal form, the numbers are 4 or 7 only.

The following are the problems.

a), Is S countable ?

b), Is it dense in XX ?

c), Is it compact ?

d), Is it perfect ?

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