ClosedInterval
Returns a closed interval of real numbers.
Syntax

ClosedInterval(a, b[, δ])

a
andb
are real numbers 
δ
is a positive number

Description
Conceptually, ClosedInterval(a, b)
returns the closed interval [a, b]. However, there are a few differences between the mathematical object [a, b] and ClosedInterval(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, ClosedInterval(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 ClosedInterval(a, b)
as the mathematical object [a, b].
Specifically, CloseInterval(a, b, δ)
returns the list of all numbers
a, a + δ, a + 2⋅δ, ...
that are less than or equal to b
. In particular, if a > b
, the empty list is returned and if a = b
, the singleelement list containing only a
is returned. Otherwise, the number of elements depends on δ
. If omitted, δ
is chosen so that the list contains about 1000 elements.
A synonym for ClosedInterval
is interval
. Also, the circumfix operator []
is mapped to this function. Hence, ClosedInterval(a, b)
can also be written interval(a, b)
or [a, b]
.
Examples
f ≔ t ↦ t⋅❨cos(t), sin(t)❩; plot([0, 6⋅π] @ f)
f ≔ t ↦ (e^sin(t) − 2⋅cos(4⋅t) + sin((2⋅t − π)/24)^5) ⋅ ❨cos(t), sin(t)❩; plot([0, 100, 0.01] @ f)