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:
“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)
“Poetry
Exceeding music must take the place
Of empty heaven and its hymns....”
—Wallace Stevens (1879–1955)
“Setting limits gives your child something to define himself against. If you are able to set limits without being overly intrusive or controlling, you’ll be providing him with a firm boundary against which he can test his own ideas.”
—Stanley I. Greenspan (20th century)