natural deduction metalanguage, practical foundations
type theory (dependent, intensional, observational type theory, homotopy type theory)
computational trinitarianism =
propositions as types +programs as proofs +relation type theory/category theory
Let $f \colon X \longrightarrow Y$ be a function between sets. Let $\{S_i \subset Y\}_{i \in I}$ be a set of subsets of $Y$. Then
$f^{-1}\left( \underset{i \in I}{\cup} S_i\right) = \left(\underset{i \in I}{\cup} f^{-1}(S_i)\right)$ (the pre-image under $f$ of a union of subsets is the union of the pre-images)
$f^{-1}\left( \underset{i \in I}{\cap} S_i\right) \subset \left(\underset{i \in I}{\cap} f^{-1}(S_i)\right)$ (the pre-image under $f$ of the intersection of the subsets is the intersection of the pre-images).
For details see at interactions of images and pre-images with unions and intersections.
Last revised on May 20, 2017 at 13:15:24. See the history of this page for a list of all contributions to it.