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Union — AI Alignment Forum

Union

Edited by M Yass, Joe Zeng, alexei, et al. last updated 3rd Oct 2016

Requires: Set

The union of two sets and $B$ , denoted $A \cup B$ , is the set of things which are either in $A$ or in $B$ or both.

illustration of the output of the union operation

Formally stated, where $B$

$x \in C \leftrightarrow (x \in A \lor x \in B)$

That is, Iff $x$ is in the union $C$ , then either $x$ is in $A$ or $B$ or possibly both.

Examples

${1, 2} \cup {2, 3} = {1, 2, 3}$

${1, 2} \cup {8, 9} = {1, 2, 8, 9}$

${0, 2, 4, 6} \cup {3, 4, 5, 6} = {0, 2, 3, 4, 5, 6}$

$R^{-} \cup R^{+} \cup {0} = R$ (In other words, the union of the negative reals, the positive reals and zero make up all of the real numbers.)

Parents:

Operations in Set theory