Axiom of Union - Formal Statement

Formal Statement

In the formal language of the Zermelo–Fraenkel axioms, the axiom reads:

or in words:

Given any set A, there is a set B such that, for any element c, c is a member of B if and only if there is a set D such that c is a member of D and D is a member of A.

Read more about this topic:  Axiom Of Union

Famous quotes containing the words formal and/or statement:

    This is no argument against teaching manners to the young. On the contrary, it is a fine old tradition that ought to be resurrected from its current mothballs and put to work...In fact, children are much more comfortable when they know the guide rules for handling the social amenities. It’s no more fun for a child to be introduced to a strange adult and have no idea what to say or do than it is for a grownup to go to a formal dinner and have no idea what fork to use.
    Leontine Young (20th century)

    No statement about God is simply, literally true. God is far more than can be measured, described, defined in ordinary language, or pinned down to any particular happening.
    David Jenkins (b. 1925)