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Topic: What does this problem mean?
Replies: 1   Last Post: Jan 31, 2013 12:02 PM

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 grei Posts: 132 Registered: 11/27/12
Re: What does this problem mean?
Posted: Jan 31, 2013 12:02 PM

> "If |P| < infinity,
This is the crucial part. This says that P is a FINITE set. Yes, "partially ordered" is all you need because the condition is "if xsubi < xsubj, then i<j". If it were the other way around, "if i<j, then xsubi < xsubj", you would need a total order because the counting numbers are ordered.

All this is saying is that BECAUSE P IS FINITE, you can look through P, find its smallest members (a member, x, such that there is NO y in the set with y< x) and call it "xsub1" through "xsubi" in whatever order you want. Then look through the remaining members to find ITS smallest remaining members, put them nest in the list, in any order, etc.

> then its elements can be ordered
> xsub1,...,xsubn so that if xsubi < xsubj, then i<j
>
> Estimate the growth (with n) of the number of such
>
> I think P is supposed to be a poset. Other than that
> I am not sure what the question is asking. Any help
> appreciated.
>
>
> Message was edited by: Alex

Date Subject Author
1/30/13 nilefan
1/31/13 grei