Closed [class]

The class splinekit.interval.Closed is the concrete class that handles the bounded intervals that are left-closed and right-closed.

This concrete class honors Interval and Bounded; it handles closed intervals between a pair of finite real numbers.

class splinekit.interval.closed.Closed(bounds: Tuple[float, float])

Bases: Interval, Bounded

The bounded interval \(\{x\in{\mathbb{R}}|x_{0}\leq x\leq x_{1}\}=[x_{0},x_{1}].\)

property infimum: float: Left endpoint.

property supremum: float: Right endpoint.

property isleftopen: bool: False

property isrightopen: bool: False

property isopen: bool: False

property ishalfopen: bool: False

property isclosed: bool: True

property isleftbounded: bool: True

property isrightbounded: bool: True

property ishalfbounded: bool: False

property isbounded: bool: True

property isdegenerate: bool: False

property isproper: bool: True

property interior: Self: Open((self.infimum, self.supremum))

property closure: Self: Closed((self.infimum, self.supremum))

property diameter: float: self.supremum - self.infimum

property midpoint: float: 0.5 * (self.supremum + self.infimum)

sortorder() → float: self.midpoint

__contains__(x: float) → bool: self.leftbound <= x <= self.rightbound

static __new__(cls, bounds: Tuple[float, float]) → Self

Creates the bounded closed interval \(\{x\in{\mathbb{R}}|x_{0}\leq x\leq x_{1}\}=[x_{0},x_{1}]\) that contains all numbers that are not smaller than \(x_{0}\) and not larger than \(x_{1}.\)

Parameters:: bounds – The tuple (infimum, supremum).
Returns:: A Closed interval if bounds contains two finite numbers, with the first number being smaller than the second; otherwise, an interval from {RR, Empty, Singleton, NotBelow, NotAbove}.
Return type:: Interval