On Jan 25, 7:52 pm, eratosthenes <rehamkcir...@gmail.com> wrote:
> She asked me if I could give her a way to explain what a mathematical > function is to a sixth grader other than the standard explanation > about it being a machine that you put one number into and receive > another out of.
Of course, I prefer the standard set theoretical definition, but that requires first defininig 'relation'.
So, how about this:
Suppose we have a set X. We say "F is a function with domain X" if for each object in X, we have F pairing it with exactly one object. In other words, if p is an object in X then F picks out some object (that we call 'F(p)') and pairs p to that object picked out. That is, for each object p in X there is exactly one object that F pairs p to. Note that if p and q are different from each other but both members of X, then a function might or might not pair p and q to the same object, but the important point is that each member of X is paired to at least one object but not to more than one object. Also point out that F might pair certain objects to themselves.
Then give an example by listing objects in some set X and drawing lines from each member of X to its value under the function. Explain that F itself is the pairing of the objects. Then give some example from everyday life that shows that each object is paired to exactly one object; show examples where an object is paired to itself; show an exmaple where different objects are paired with the same object. Show an example where no two different objects happen to pair to the same object.
Or give the examples before the abstract explanation, then, to reinforce, go back to the examples after having given the abstract explanation.