a. all bit strings not containing the bit 0  b. all positive rational numbers that cannot be written with denominators less than 4  c. the real numbers not containing 0 in their decimal representation  d. the real numbers containing only a finite number of 1s in their decimal representation

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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Determine  whether  each  of  these  sets  is  countable  or  uncountable.  For  those  that  are 
countably infinite, exhibit a one-to-one correspondence between the set of positive integers 
and that set.         
a. all bit strings not containing the bit 0 
b. all positive rational numbers that cannot be written with denominators less than 4 
c. the real numbers not containing 0 in their decimal representation 
d. the real numbers containing only a finite number of 1s in their decimal representation 

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The problem is from set, cardinality and topology.

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