Axiom of Empty Set

In axiomatic set theory, the axiom of empty set is an axiom of Kripke–Platek set theory and the variant of general set theory that Burgess (2005) calls "ST," and a demonstrable truth in Zermelo set theory and Zermelo–Fraenkel set theory, with or without the axiom of choice.

Read more about Axiom Of Empty Set:  Formal Statement, Interpretation

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    It’s an old axiom of mine: marry your enemies and behead your friends.
    —Robert N. Lee. Rowland V. Lee. King Edward IV (Ian Hunter)

    “You are bothered, I suppose, by the idea that you can’t possibly believe in miracles and mysteries, and therefore can’t make a good wife for Hazard. You might just as well make yourself unhappy by doubting whether you would make a good wife to me because you can’t believe the first axiom in Euclid. There is no science which does not begin by requiring you to believe the incredible.”
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    And I think in this empty world there was room for me and a
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    And I think in the world beyond, how easily we might spare a million
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    The spirit of [William] Penn will not be stayed. You cannot set limits to such knightly adventurers. After their own day is gone their spirits stalk the world, carrying inspiration everywhere that they go and reminding men of the lineage, the fine lineage, of those who have sought justice and right.
    Woodrow Wilson (1856–1924)