Above [class]

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

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

class splinekit.interval.above.Above(threshold: float)

Bases: Interval, HalfBounded

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

property infimum: float: self.threshold

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

property isleftopen: bool: True

property isrightopen: bool: True

property isopen: bool: True

property ishalfopen: bool: False

property isclosed: bool: False

property isleftbounded: bool: True

property isrightbounded: bool: False

property ishalfbounded: bool: True

property isbounded: bool: False

property isdegenerate: bool: False

property isproper: bool: True

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

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

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

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

sortorder() → float: self.threshold

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

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

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

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