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)
“The writer who neglects punctuation, or mispunctuates, is liable to be misunderstood.... For the want of merely a comma, it often occurs that an axiom appears a paradox, or that a sarcasm is converted into a sermonoid.”
—Edgar Allan Poe (1809–1845)
“Boy, I hate their empty shows,
Persian garlands I detest,
Bring me not the late-blown rose
Lingering after all the rest:
Plainer myrtle pleases me
Thus outstretched beneath my vine,
Myrtle more becoming thee,
Waiting with thy master’s wine.”
—Horace [Quintus Horatius Flaccus] (65–8)
“Really, if the lower orders don’t set us a good example, what on earth is the use of them? They seem, as a class, to have absolutely no sense of moral responsibility.”
—Oscar Wilde (1854–1900)