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Mathematics

The Axiom of Choice and Its Surprising Consequences

Quick fact

The Axiom of Choice was once so controversial that some mathematicians refused to use it because of its paradoxical consequences, like the Banach-Tarski paradox, which shows a sphere can be cut into pieces and reassembled into two identical spheres.

Why this is interesting

Imagine you have an infinite number of boxes, each containing at least one item. Can you select one item from each box? Sounds easy, right? But what if there is no rule to tell you which one to pick?