FrediFizzx wrote:Joy Christian wrote:No. That is not what I am saying. For any functions f and g, if < f > = < g >, then that does not imply f = g. It does not matter what f and g are. A specific example does not change this.

Well, you are going to have to prove that. I'm not buying it.

It is a trivial fact and easy to prove using counterexamples.

One counterexample is sufficient to prove it.

Your claim is that < f > = < g > --> f = g.

So let f = 1 + cos(x) and g = 1 + sin(x), with 0 < x < 360 degrees.

Then < f > = 1 = < g >, where average is over all angles x.

This, according to your claim, implies f = g.

But it is self-evident that f =/= g.

So your claim is wrong (by

reductio ad absurdum).

.