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I have a set $ X = \{a,b,c,d\} $ where all elements of the set are tuples $ (x,y), x \in \mathbb{N}, y \in \mathbb{N} $. In this case the elements of the tuple would represent a timeslot where start time x and an end time y. I know want to have a constraint that compares all elements to each other, so that no timeslot in the set is overlapping. Basically $ y_1 > x_2 \vee x_1 > y_2 $. How would I go to describe this mathematically?

nino
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    You could say that $X$ is totally ordered by the relation $<$, where $(x_1, y_1)<(x_2, y_2)$ iff $y_1<x_2$, with respect to the order $<$ on $\mathbb N$. (I guess you're assuming $y_1>x_i$ for all intervals in $X$?) – Nishant Nov 23 '14 at 14:44

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