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What do you mean by the term strict part of a binary relation?

How can it be used to define minimal element for any set with relation?

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    example:to get strict part of binary relation that is called partial order ($\leq$) one has to remove such $(a,b)$ pairs where $a=b$2011-10-08

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It's hard to say without more context, but it seems like you are to take out pairs of the form $(x,x)$ from your relation (i.e. dropping the condition of reflexivity). This is similar to how "less than or equal to" gives rise to "strictly less than".

Given a strict relation, you can find a minimal element of a finite set by taking a descending chain $x_1 > x_2 > \cdots > x_n$. Since the set is finite, the chain will indeed terminate at a minimal element.

If the set is infinite, there may not be a minimal element under every relation. For example, in the real numbers with usual "less than" relation there can be descending chains with no minimal element.

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    I haven't heard the term before, but this is what I would immediately assume it means, for precisely the reason given here.2011-10-09