Real Interval


Real Interval is a direct subtype of Math
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with functions Real Interval Functions, keys Real Interval keys and example object (0,1)

TYPE INCLUSION RELATIONSHIPS

Math

Real Interval

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AVAILABLE FUNCTIONS

Are Distinct

Complement

Create

Cross Section

Difference

Is Contained

Sort

Stacked Covered Subintervals

Union

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AVAILABLE CREATE FUNCTION KEYS

Borders

Left

Right

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TYPICAL OBJECTS OF TYPE Real Interval

RealInterv

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This type represents a one-dimensional real interval - i.e. an interval of real numbers - characterized by two boundary real numbers, the left boundary a and the right boundary b together with a rule that governs the inclusion of a and b in the interval, which rule is a choice from Interval Borders

One or both of the numbers a and b may be omitted.
If a is omitted, the left boundary becomes (-∞ and must be open, i.e. denoted with a left parentesis.
If b is omitted, the right boundary becomes +∞) and must be open, i.e. denoted with a right parentesis.

All Real Interval objects are trivial objects and as such can be automatically generated from appropriately formatted text prefixed with the symbol %
Given the numbers a and b, the text must have one of the following 4 forms:
%(a,b) when neither a nor b belong to the interval.
%[a,b) when only a belongs to the interval.
%(a,b] when only b belongs to the interval.
%[a,b] when both a and b belong to the interval.

The following variations apply when either a or b or both are left unspecified, as mentioned above:
%(,b) which represents the interval (-∞,b)
%(,b] which represents the interval (-∞,b]
%(a,) which represents the interval (a,+∞)
%[a,) which represents the interval [a,+∞)
%(,) which represents the interval (-∞,+∞)

Note that spaces are not allowed.

It is possible to generate intervals such (2,1) or (1,1) or [1,1), but all such intervals are considered equal to the void interval, i.e. the special interval that contains no number.

Also the numbers a and b must be represented in the US format, i.e. a number such as ½ must appear as 0.5 or .5 but never as 0,5 even if the locale is non-US.