Set Theory Question
 

I have a question abouts partially ordered sets (posets). Can a poset with an infinite number of members ever be well-founded?

Re: Set Theory Question
 

[QUOTE][i]Originally posted by jwsiii [/i]
[B]I have a question abouts partially ordered sets (posets). Can a poset with an infinite number of members ever be well-founded? [/B][/QUOTE]

um... yeah, the positive integers are a well-founded infinite poset. perhaps you can say a little more about what you want to know?

I'm just learning about relations, posets, wosets, etc and I'm trying to understand them better. Would an infinite poset like { 34, 33, 32, ... -478, -479, ... } be well-founded? If the numbers are decreasing, wouldn't there never be a minimal element?

[QUOTE][i]Originally posted by jwsiii [/i]
[B]I'm just learning about relations, posets, wosets, etc and I'm trying to understand them better. Would an infinite poset like { 34, 33, 32, ... -478, -479, ... } be well-founded? If the numbers are decreasing, wouldn't there never be a minimal element? [/B][/QUOTE]

this set would not be well-founded, at least not under the normal ordering of integers. but in general a set may admit many orderings, and by the axiom of choice, there is always some ordering under which the set obeys the well-ordering principle, infinite or finite.