Shows three mappings (each on an own page) from the set <i>E</i> of even numbers to the set <i>N</i> of natural numbers, with different properties w.r.t. surjectivity and injectivity. Since some surjective and injective mapping from <i>E</i> to <i>N</i> exists, both are of same cardinality by definition. — In contrast, for any finite sets <i>A</i> and <i>B</i>, if a surjective and injective mapping from <i>A</i> to <i>B</i> exists, then (both are of same cardinality again, and hence) each mapping from <i>A</i> to <i>B</i> is surjective iff it is injective.
<a href="//commons.wikimedia.org/wiki/User:Jochen_Burghardt" title="User:Jochen Burghardt">Jochen Burghardt</a>
CC BY-SA 4.0
<span class="int-own-work" lang="en">Own work</span>