The first sentence is false, and it should be obvious that it is false. It may appearOriginally Posted bysteve bankto youthat that is so, because you believe that I'm saying something very different from what I'm saying. But that is not on me.

The second sentence has the problem of lacking parentheses, but it is obviously true that (-1)^3=(-1)*(-1)*(-1)=-1 (well, it is obvious to me anyway).

That is correct.Originally Posted bysteve bank

Of course I reject nothing of the sort.Originally Posted bysteve bank

I already have, and this seems pointless because you are failing to follow, but here goes again: There is no function f from a domain D into the complex numbers with the following properties:Originally Posted bysteve bank

1. D contains the real line.

2. For all nonnegative real x, f(x)=sqrt(x).

3. For all x,y in D, f(xy)=f(x)f(y).

4. For all x in D, (f(x))^2=x.

This is the sort of function that would extend the usual sqrt function, defined for nonnegative reals, and keeping some nice properties used in SLD's proof.

By the way, SLD's proof is actually a proof by contradiction that there is no such function. It's just that SLD (just for fun, because he understands it) reached the opposite conclusion, i.e., that 1=-1. I took this thread also to be for fun (hence, my first reply), but you made it contentious for some reason.