Definition:Induced Operation

From ProofWiki
Jump to navigation Jump to search

Disambiguation

This page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.

Induced Operation may refer to:


$A \circ_\mathcal P B = \left\{{a \circ b: a \in A, b \in B}\right\}$


$\left[\!\left[{x}\right]\!\right]_\mathcal R \circ_\mathcal R \left[\!\left[{y}\right]\!\right]_\mathcal R = \left[\!\left[{x \circ y}\right]\!\right]_\mathcal R$


$\left({s_1, s_2, \ldots, s_n}\right) \circ \left({t_1, t_2, \ldots, t_n}\right) := \left({s_1 \circ_1 t_1, s_2 \circ_2 t_2, \ldots, s_n \circ_n t_n}\right)$ for all ordered $n$-tuples in $S$


$f \oplus g: S \to T: \forall x \in S: \left({f \oplus g}\right) \left({x}\right) = f \left({x}\right) \circ g \left({x}\right)$