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Nov19-07, 11:33 PM
P: 45
The new set, [tex] f(a) [/tex], is a set consisting of all [tex] x \epsilon A [/tex] s.t. [tex] x \leq a [/tex].

For example, consider [tex] A = \mathbb{N} [/tex]. Look at [tex] f(5) [/tex]. This is simply [tex] \{1,2,3,4,5\} [/tex].

So, for the first part, you need to show that

[tex] f(a)=f(b) \Rightarrow a=b [/tex]

I'll stop here, just in case you need more assistance.