A set is countably infinite if its elements can be put in one-to-one correspondence with the set of natural numbers. In other words, one can count off all elements in the set in such a way that, even though the counting will take forever, you will get to any particular element in a finite amount of time.

What is an example of an uncountable infinite set?

Mathwords: Uncountable. Describes a set which contains more elements than the set of integers. Formally, an uncountably infinite set is an infinite set that cannot have its elements put into one-to-one correspondence with the set of integers. For example, the set of real numbers is uncountably infinite.

Is Z+ countably infinite?

The symbol Z+ denotes the set of positive integers. ... A set A is countably infinite if there exists a bijection f : Z+ → A.