Axiom of Choice
The axiom of choice is equivalent to the statement that the product of a collection of non-empty sets is non-empty. The proof is easy enough: one needs only to pick an element from each set to find a representative in the product. Conversely, a representative of the product is a set which contains exactly one element from each component.
The axiom of choice occurs again in the study of (topological) product spaces; for example, Tychonoff's theorem on compact sets is a more complex and subtle example of a statement that is equivalent to the axiom of choice.
Read more about this topic: Product Topology
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—Robert N. Lee. Rowland V. Lee. King Edward IV (Ian Hunter)
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“Holofernes. He is too picked, too spruce, too affected, too odd as it were, too peregrinate as I may call it.
Sir Nathaniel. A most singular and choice epithet.”
—William Shakespeare (1564–1616)