NotAbove [class]

The class splinekit.interval.NotAbove is the concrete class that handles the right-bounded half-bounded intervals that are not right-open.

This concrete class honors Interval and HalfBounded; it handles right-bounded intervals not above a finite real number.

class splinekit.interval.not_above.NotAbove(threshold: float)

Bases: Interval, HalfBounded

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

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

property supremum: float: self.threshold

property isleftopen: bool: True

property isrightopen: bool: False

property isopen: bool: False

property ishalfopen: bool: True

property isclosed: bool: True

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 \(\{x\in{\mathbb{R}}|x\leq x_{0}\}=(—\infty,x_{0}]\) that contains all numbers that are not larger than the threshold \(x_{0}.\)

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