Revision as of 16:32, 31 March 2025 edit Remsense (talk \| contribs) Extended confirmed users, Page movers, New page reviewers, Pending changes reviewers, Template editors 95,470 edits Adding intentionally blank description Tag: Shortdesc helper ← Previous edit		Latest revision as of 22:58, 2 May 2025 edit undo Rgdboer (talk \| contribs) Autopatrolled, Extended confirmed users, Pending changes reviewers 18,111 edits m →Related definitions: semicolon is traditional symbol for composition of relations
Line 66: The '''downward closure''' of a member <math>x</math> of the field of <math>R</math> is the smallest set <math>D</math> containing <math>x</math>, and containing each <math>zRy</math> for each <math>y \in D</math> (i.e., including the preimage of each of its elements with respect to <math>R</math> as a subset.) The '''[[relation composition\|relative product]]''' <math>R\|;S</math> of <math>R</math> and <math>S</math> is the relation <math>\left\{\left(x, z\right) : \exists y\,\left(xRy \wedge ySz\right)\right\}</math>. Notice that with our formal definition of a binary relation, the range and codomain of a relation are not distinguished. This could be done by representing a relation <math>R</math> with codomain <math>B</math> as <math>\left(R, B\right)</math>, but our development will not require this.

Implementation of mathematics in set theory: Difference between revisions