Answer:
a) the negative integers set A is countably infinite.
one-to-one correspondence with the set of positive integers:
f: Z+ → A, f(n) = -n
b) the even integers set A is countably infinite.
one-to-one correspondence with the set of positive integers:
f: Z+ → A, f(n) = 2n
c) the integers less than 100 set A is countably infinite.
one-to-one correspondence with the set of positive integers:
f: Z+ → A, f(n) = 100 - n
d) the real numbers between 0 and 12 set A is uncountable.
e) the positive integers less than 1,000,000,000 set A is finite.
f) the integers that are multiples of 7 set A is countably infinite.
one-to-one correspondence with the set of positive integers:
f: Z+ → A, f(n) = 7n
Step-by-step explanation:
A set is finite when its elements can be listed and this list has an end.
A set is countably infinite when you can exhibit a one-to-one correspondence between the set of positive integers and that set.
A set is uncountable when it is not finite or countably infinite.
