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)
“It is an axiom in political science that unless a people are educated and enlightened it is idle to expect the continuance of civil liberty or the capacity for self-government.”
—Texas Declaration of Independence (March 2, 1836)
“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)
“The lady—bearer of this—says she has two sons who want to work. Set them at it, if possible. Wanting to work is so rare a merit, that it should be encouraged.”
—Abraham Lincoln (1809–1865)