I want to show that {1,2}×Z+ and Z+×{1,2} have different order type
If we define f(i,j)=(j,i) for i in {1,2} and j in Z+
It seems like that this is bijective map between two sets.
However, to show that they are not order isomorphic, how shall I start to show that bijection does not preserve ordering?
It seems like that the way I defined the bijection is not the only way.
I am wondering if there exists any bijection between two sets and that bijection does not preserve order, can I conclude that they have different order type?
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