/docs/projects_math_docs_docs.output/projects_math_docs_pure_pure.output/ Recent content in Pure Math on tplat Hugo en /docs/projects_math_docs_docs.output/projects_math_docs_pure_pure.output/sets/ Mon, 01 Jan 0001 00:00:00 +0000 /docs/projects_math_docs_docs.output/projects_math_docs_pure_pure.output/sets/ <h1 id="sets">Sets<a class="anchor" href="#sets">#</a></h1> <p>A set is just a collection of distinct objects.</p> <p>Examples:</p> <ul> <li>$\mathbb{R}$: real numbers</li> <li>$\{1,2,3\}$</li> <li>solutions to an equation</li> </ul> <p>In pure math, you define things by properties, not construction.</p> /docs/projects_math_docs_docs.output/projects_math_docs_pure_pure.output/functions/ Mon, 01 Jan 0001 00:00:00 +0000 /docs/projects_math_docs_docs.output/projects_math_docs_pure_pure.output/functions/ <h1 id="functions">Functions<a class="anchor" href="#functions">#</a></h1> <p>A function $f: A \to B$ is:</p> <ul> <li>a set $A$ (domain)</li> <li>a set $B$ (codomain)</li> <li>a rule assigning <strong>each element</strong> of $A$ to <strong>exactly one</strong> element of $B$ <ul> <li>many elements of $A$ may beassigned to one element of $B$, but to <strong>only one element</strong> of $B$</li> </ul> </li> </ul> /docs/projects_math_docs_docs.output/projects_math_docs_pure_pure.output/logic/ Mon, 01 Jan 0001 00:00:00 +0000 /docs/projects_math_docs_docs.output/projects_math_docs_pure_pure.output/logic/ <h1 id="logic">Logic<a class="anchor" href="#logic">#</a></h1> <h2 id="implication">Implication<a class="anchor" href="#implication">#</a></h2> <p><em>If $P$, then $Q$</em>; written as $P \implies Q$</p> <blockquote class='book-hint '> <p>Whenever $P$ is true, then $Q$ must also be true</p></blockquote>