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.
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Famous quotes containing the words axiom of, axiom, empty and/or set:
“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.””
—Henry Brooks Adams (1838–1918)
“It is difficult to read. The page is dark.
Yet he knows what it is that he expects.
The page is blank or a frame without a glass
Or a glass that is empty when he looks.”
—Wallace Stevens (1879–1955)
“Here did she fall a tear. Here in this place
I’ll set a bank of rue, sour herb-of-grace.
Rue even for ruth here shortly shall be seen
In the remembrance of a weeping queen.”
—William Shakespeare (1564–1616)