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posted by  justjilly3 on 10/10/2008 12:43:14 AM  |  status: Live  

Discrete Mathematics and Its Applications

Course Textbook Chapter Problem
Discrete Math Discrete Mathematics and Its Applications, 6th, Rosen 2.4 34
Question Details:
Determine whether each of these sets is countable or uncountable. For those that are countable, exhibit a one-to-one correspondence between the set of natural number and that set.

a) integers not divisible by 3
b) integers divisible by 5 but not by 7
c) the real numbers with decimal representations consisting of all 1s
d) the real numbers with decimal representations of all 1s or 9s
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posted by kajikunido on 10/10/2008 5:19:17 AM  |  status: Live
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Response Details:
a and b are countable
c and d are uncountable
 
Naturals are an infinite yet countable set and Integers are equivalent to Naturals, which means that Integers are countable as well, so any set within Integers is also countable, which is why a and b are countable.
 
Reals are never countable, because whatever decimal you get, you can always add infinite digits behind that decimal.
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