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Non-strict partial order
Definition
| $X$ |
| $ \le\ \in\ \mathrm{it} $ |
The relation $\le$ is an order relation if it's in the intersection of all reflexive, all anti-symmetric and all transitive relation. Hence
| $ \le\ \in\ \mathrm{Rel}(X) $ |
| $ x,y,z \in X $ |
| $ x \le x $ |
| $ x\le y\ \land\ y\le x \implies (x=y) $ |
| $ x \le y\ \land\ y \le z \Leftrightarrow x\le z $ |
Here we use infix notation: $x\le y\ \equiv\ \le(x,y)$.
Discussion
Reference
Wikipedia: Order theory, Poset
Context
Subset of
