# Order Preserving Bijection

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.

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 $$a-1, so what must be true of $$n$$ if $$f$$ is to be order-preserving?