Well ordered set

Deadstar · #1 $Old$ November 2nd, 2009, 04:24 PM

Suppose $(A,\leq)$ is a well-ordered set. Let $B = \mathbb{R}^A$ . Find an explicit linear order on $B$ .

So I have to prove reflexivity, antisymmetry, transitivity and that B is linear. Thing is I cant really get my head around what $B = \mathbb{R}^A$ actually is... Set of functions from A to $\mathbb{R}$ . But A is well ordered... So how does that change things?

Does this involve creating an in/bijection between B and some well ordered set?

whatisthisfor · #2 $Old$ November 3rd, 2009, 03:36 AM

clic-clac explained how to form the linear order pretty well for me:

Finding a linear order on a set

proving the rest is a bit easier.

Now, know anything about question 4?

Ordinal Arithmetic