Definition:Interval/Notation/Unbounded Intervals
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Definition
In Wirth interval notation, unbounded intervals of an ordered set $\struct {S, \preccurlyeq}$ are written as follows:
| \(\ds \hointr a \to\) | \(:=\) | \(\ds \set {x \in S: a \preccurlyeq x}\) | ||||||||||||
| \(\ds \hointl \gets a\) | \(:=\) | \(\ds \set {x \in S: x \preccurlyeq a}\) | ||||||||||||
| \(\ds \openint a \to\) | \(:=\) | \(\ds \set {x \in S: a \prec x}\) | ||||||||||||
| \(\ds \openint \gets a\) | \(:=\) | \(\ds \set {x \in S: x \prec a}\) | ||||||||||||
| \(\ds \openint \gets \to\) | \(:=\) | \(\ds \set {x \in S} = S\) |