axioms of choice

The Axiom of Choice is a principle in mathematics stating that given any collection of non-empty sets, it’s possible to select exactly one element from each set, even if the collection is infinite or lacks an explicit rule for making the selection. This means that, theoretically, a choice function exists for any such collection. It’s fundamental for certain areas of mathematics, enabling proofs that would otherwise be impossible, but it’s non-constructive; it doesn’t specify how to make the choices, only that such a selection can exist.