Hello

Here is a problem I am doing. Suppose and let

.

Let

Prove that and therefore .

Velleman gives some hints at the back of the book. To prove ,

he suggets a function defined as

.

He suggets some things to prove that h is one to one. I could do that. Now to prove

that h is onto, he says , suppose R is a total order on A. Define

by the formula .

He asks the reader to show that

I could show this. Then he says use this fact to show that

and . I could show that g is one to one. To prove that

, I should also show that g is onto. But I have not been able

to show this. Input is welcome.