- #1
g1990
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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+