Axiom of choice

In mathematics the axiom of choice, sometimes called AC, is an axiom used in set theory.

The axiom of choice says that if you have a group of sets , each containing at least one object, it is possible to take one object out of each of these smaller sets and make a new set. You do not always need to use the axiom of choice to do this. You do not need to use the axiom of choice if the starting set is finite, or if the starting set is infinite and has a rule built in for how it can be divided. For example you could select the smallest number in every set without using the axiom of choice even if there are infinite sets. A non mathematical example would be for any (infinite or finite) collection of pairs of shoes, you can pick out the left shoe from each pair, but for an infinite collection of pairs of socks, you could not do this as there is no left or right sock and so would need the axiom of choice.