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

e) the positive integers less than 1,000,000,000

f) the integers that are multiples of 7

SOLUTION

Step 1

We have to check the following sets are finite, countably infinite, or uncountable.