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:

    The spiritual kinship between Lincoln and Whitman was founded upon their Americanism, their essential Westernism. Whitman had grown up without much formal education; Lincoln had scarcely any education. One had become the notable poet of the day; one the orator of the Gettsyburg Address. It was inevitable that Whitman as a poet should turn with a feeling of kinship to Lincoln, and even without any association or contact feel that Lincoln was his.
    Edgar Lee Masters (1869–1950)

    The force of truth that a statement imparts, then, its prominence among the hordes of recorded observations that I may optionally apply to my own life, depends, in addition to the sense that it is argumentatively defensible, on the sense that someone like me, and someone I like, whose voice is audible and who is at least notionally in the same room with me, does or can possibly hold it to be compellingly true.
    Nicholson Baker (b. 1957)