If all real numbers were to be multiplied to each other, what would be the product?

(a) Undefined

(b) Imaginary Number

(c) None of these

(In reply to

Another opinion by Steve Herman)

I really don't understand how to approach this problem. But as for the pairing stuff - I can see that for the interval 0<x<1 there would be a

corresponding interval 1<1/x< infinity (and likewise on the other side of 0). As for 1/2x, I don't no know where one would start so as to fill up the number line.

But moreover I don't know that any of this makes any sense. Does it have anything to do with conformal mapping? Is there a way to show the answer (excluding zero) is undefined. Is the answer including zero actually zero or is that undefined too?