If a function is both one-to-one and onto it is called a one-to-one correspondence or a bijection.
Exercise: Construct a function on the integers that is onto but not one-to-one. (possible solution)
Exercise: Construct a function on the integers that is one-to-one but not onto. (possible solution)
</td><td>=</td><td><img src=bigleftbrace.png></td><td>0 if <em>x</em> is odd<br><em>x</em>/2 if <em>x</em> is even.</td></tr></table>')){kind=link}
</td><td>=</td><td><img src=bigleftbrace.png></td><td><em>x</em> if <em>x</em><0<br><em>x</em>+1 if <em>x</em>≥0</td></tr></table>')){kind=link}