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Determine whether each of these sets is finite, countably
Chapter 2, Problem 1E(choose chapter or problem)
Determine whether each of these sets is finite, countably infinite, or uncountable. For those that are countably infinite, exhibit a one-to-one correspondence between the set of positive integers and that set.
a) the negative integers
b) the even integers
c) the integers less than \(100\)
d) the real numbers between 0 and \(\frac{1}{2}\)
e) the positive integers less than \(1,000,000,000\)
f) the integers that are multiples of \(7\)
Equation Transcription:
Text Transcription:
100
1/2
1,000,000,000
7
Questions & Answers
QUESTION:
Determine whether each of these sets is finite, countably infinite, or uncountable. For those that are countably infinite, exhibit a one-to-one correspondence between the set of positive integers and that set.
a) the negative integers
b) the even integers
c) the integers less than \(100\)
d) the real numbers between 0 and \(\frac{1}{2}\)
e) the positive integers less than \(1,000,000,000\)
f) the integers that are multiples of \(7\)
Equation Transcription:
Text Transcription:
100
1/2
1,000,000,000
7
ANSWER:
SOLUTION
Step 1
We have to check the following sets are finite, countably infinite, or uncountable.