OpenInterval
Returns an open interval of real numbers.
Syntax

OpenInterval(a, b[, δ])

a
andb
are real numbers 
δ
is a positive number

Description
Conceptually, OpenInterval(a, b)
returns the open interval (a, b). However, there are a few differences between the mathematical object (a, b) and OpenInterval(a, b)
.
First, since the mathematical set (a, b) contains an infinite number of real numbers when a < b (the typical case), it cannot be represented as a true Algosim set, since that would require a computer with an infinite amount of memory. Therefore, OpenInterval(a, b)
only returns a finite number of equally spaced numbers from this interval.
Second, the returned object isn’t an Algosim set but a list. This is because lists are easier to work with in practice. Still, Algosim is designed in such a way that you often can think of OpenInterval(a, b)
as the mathematical object (a, b).
Specifically, OpenInterval(a, b, δ)
returns the list of all numbers
a + δ, a + 2⋅δ, ...
that are less than or equal to b − δ
. In particular, if a ≥ b
, the empty list is returned. Otherwise, the number of elements depends on δ
. If omitted, δ
is chosen so that the list contains about 1000 elements.