Math CentralQuandaries & Queries


Question from Lucy, a student:

How can a function relate each element of a set with exactly one element of possibly the same set?

Hi Lucy,

Suppose that $A$ is the set with two elements $a$ and $b$ and $P$ is the set with elements $p$ and $q.$ You could definf the function $f$ from $A$ to $P$ by $f(a) = q \mbox{ and } f(b) = p.$ Can you find a different function? What if $P$ is the same set as $A?$


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