Returns an open interval of real numbers.
OpenInterval(a, b[, δ])
bare real numbers
δis a positive number
OpenInterval(a, b) returns the open interval (a, b). However, there are a few differences between the mathematical object (a, b) and
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).
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.