﻿ OpenInterval – Algosim documentation
Algosim documentation: OpenInterval

# OpenInterval

Returns an open interval of real numbers.

## Syntax

• `OpenInterval(a, b[, δ])`

• `a` and `b` 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.