Axiom of Choice/Examples

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Examples of Use of Axiom of Choice

Russell's Socks and Shoes

Suppose we have an infinite number of pairs of socks.

Using the Axiom of Choice, we can simultaneously pick one sock from each pair.


However, if we also have a infinite number of pairs of shoes, we no longer need the Axiom of Choice to pick one shoe from each pair.

We simply choose the left one.