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Consider the posets $(\mathbb{Z}^+,\leq)$ and $(\mathbb{Z}^-,\leq)$. Is the bijection $f: \mathbb{Z}^+ \rightarrow \mathbb{Z}^-$ not order preserving?

I am new to set theory and I don't have an idea on how to show whether $f$ is order preserving. Any help will be highly appreciated.

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HINT: There is no order-preserving bijection $f:\Bbb Z^+\to\Bbb Z^-$. Suppose that $f(1)=a$, where $a$ is some negative integer. If $f$ is a bijection, there must be some positive integer $n$ such that $f(n)=a-1$. And $a-1<a$, so what must be true of $n$ if $f$ is to be order-preserving?

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