Axiom of Empty Set

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)

    To people off alone, as we were, there is something stirring about finding evidences of human labour and care in the soil of an empty country. It comes to you as a sort of message, makes you feel differently about the ground you walk over every day.
    Willa Cather (1873–1947)

    We set up a certain aim, and put ourselves of our own will into the power of a certain current. Once having done that, we find ourselves committed to usages and customs which we had not before fully known, but from which we cannot depart without giving up the end which we have chosen. But we have no right, therefore, to claim that we are under the yoke of necessity. We might as well say that the man whom we see struggling vainly in the current of Niagara could not have helped jumping in.
    Anna C. Brackett (1836–1911)