Thread: Partially ordered set View Single Post
 P: 45 The new set, $$f(a)$$, is a set consisting of all $$x \epsilon A$$ s.t. $$x \leq a$$. For example, consider $$A = \mathbb{N}$$. Look at $$f(5)$$. This is simply $$\{1,2,3,4,5\}$$. So, for the first part, you need to show that $$f(a)=f(b) \Rightarrow a=b$$ I'll stop here, just in case you need more assistance.