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## Homework Statement

Both {1,2}x Z+ and Z+ x {1,2} are well-ordered in the dictionary order. Are they of the same order type? Why or why not?

## Homework Equations

To be of the same order type, we must be able to construct a bijection that preserves order, that is, x<y => f(x)<f(y). well-ordered means that every nonempty subset has a minimal element.

## The Attempt at a Solution

I know I need to find a bijection between the two, but I can't seem to think of one. I can get a bijection from Z+ x {1,2} to Z+, but I can't find one from the other one to Z+