First, let us recall the modern notion of a function. A function is a set of ordered pairs. If &lt;a,b&gt; is in a function f, this means that the value of f for the argument a is b or, more concisely, f(a) = b. By the mathematical definition of a function, for each argument of a function there is one and only one value. So, if the ordered pair &lt;a,b&gt; is in a function f and so is &lt;a,c&gt;, then b is the same thing as c.