Below [class]

The class splinekit.interval.Below is the concrete class that handles the right-bounded half-bounded intervals that are right-open.

This concrete class honors Interval and HalfBounded; it handles right-bounded intervals below a finite real number.

class splinekit.interval.below.Below(threshold: float)

Bases: Interval, HalfBounded

The left-unbounded interval \(\{x\in{\mathbb{R}}|x<x_{0}\}=(—\infty,x_{0}).\)

property infimum: float: float("-inf")

property supremum: float: self.threshold

property isleftopen: bool: True

property isrightopen: bool: True

property isopen: bool: True

property ishalfopen: bool: False

property isclosed: bool: False

property isleftbounded: bool: False

property isrightbounded: bool: True

property ishalfbounded: bool: True

property isbounded: bool: False

property isdegenerate: bool: False

property isproper: bool: True

property interior: Self: Below(self.threshold)

property closure: Self: NotAbove(self.threshold)

property diameter: float: float("inf")

property midpoint: float: float("nan")

sortorder() → float: self.threshold

__contains__(x: float) → bool: math.isfinite(x) and (x < self.threshold)

static __new__(cls, threshold: float) → Self

Creates the left-unbounded interval \(\{x\in{\mathbb{R}}|x<x_{0}\}=(—\infty,x_{0})\) that contains all numbers that are smaller than the threshold \(x_{0}.\)

Parameters:: threshold – The threshold below which every number belongs to this interval.
Returns:: A Below interval if threshold is a finite number; RR() if threshold == float("inf"); and the Empty interval otherwise.
Return type:: Interval