Defining functions from A/R to X

From CS2800 wiki

Often, we want to define functions from [math]A/R [/math] to another set [math]X [/math] by giving their values on representatives. For example, we might wish to define a function from the set of families to the set of eye colors by defining [math]f([a]) := a\text{'s eye color} [/math].

However, this does not give a well-defined function, because we can choose different representatives [math]a [/math] and [math]a' [/math] of the same family, and [math]f [/math] would give different values for the two representatives. For [math]f [/math] to be a function, it would need to be unambiguous.

Therefore, when defining a function [math]f [/math] in this way, it is important to check that if [math]\href{/cs2800/wiki/index.php/%E2%9F%A6a%E2%9F%A7_R}{⟦a⟧_R} = \href{/cs2800/wiki/index.php/%E2%9F%A6a%E2%9F%A7_R}{⟦a'⟧_R} [/math] (in other words, if [math]\href{/cs2800/wiki/index.php/XRy}{aRa'} [/math]) then [math]f(\href{/cs2800/wiki/index.php/%E2%9F%A6a%E2%9F%A7_R}{⟦a⟧_R}) = f(\href{/cs2800/wiki/index.php/%E2%9F%A6a%E2%9F%A7}{⟦a'⟧_R}) [/math].