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
Famous quotes containing the words axiom of, axiom, empty and/or set:
“Its 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 cant possibly believe in miracles and mysteries, and therefore cant 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 cant believe the first axiom in Euclid. There is no science which does not begin by requiring you to believe the incredible.”
—Henry Brooks Adams (18381918)
“And I think in this empty world there was room for me and a
mountain lion.
And I think in the world beyond, how easily we might spare a million
or two of humans
And never miss them.”
—D.H. (David Herbert)
“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 (18561924)