https://courses.cs.cornell.edu/cs2800/wiki/index.php?title=Proof:Cardinality_of_evens&feed=atom&action=history Proof:Cardinality of evens - Revision history 2022-09-30T12:50:48Z Revision history for this page on the wiki MediaWiki 1.30.0 https://courses.cs.cornell.edu/cs2800/wiki/index.php?title=Proof:Cardinality_of_evens&diff=1618&oldid=prev Mdg39: Created page with "{{:Claim:cardinality of evens}} {{Proof|1=cardinality of evens|2= Let [itex]f : X → ℕ[/itex] be given by [itex]f(2n) := n[/itex]. [itex]f[/itex] is clearly a w..." 2018-05-28T14:33:23Z <p>Created page with &quot;{{:Claim:cardinality of evens}} {{Proof|1=cardinality of evens|2= Let &lt;math&gt;f : X <a href="/cs2800/wiki/index.php/%E2%86%92" title="→">→</a> <a href="/cs2800/wiki/index.php/%E2%84%95" title="ℕ">ℕ</a>&lt;/math&gt; be given by &lt;math&gt;f(2n) := n&lt;/math&gt;. &lt;math&gt;f&lt;/math&gt; is clearly a w...&quot;</p> <p><b>New page</b></p><div>{{:Claim:cardinality of evens}}<br /> <br /> {{Proof|1=cardinality of evens|2=<br /> Let &lt;math&gt;f : X [[→]] [[ℕ]]&lt;/math&gt; be given by &lt;math&gt;f(2n) := n&lt;/math&gt;. &lt;math&gt;f&lt;/math&gt; is clearly a [[well-defined]] [[function]], because [[every]] [[element]] of the [[domain]] is of the form &lt;math&gt;2n&lt;/math&gt; [[there exists|for]] [[unique|exactly one]] &lt;math&gt;n&lt;/math&gt;. It is also clearly a bijection (details left as an exercise). Thus the [[even]]s and the [[natural number|naturals]] have the same [[cardinality]].<br /> }}</div> Mdg39