﻿ ≤ – Algosim documentation
Algosim documentation: ≤

# ≤ (less-than or equal to)

The less than or equal to relational operator.

## Syntax

• `a ≤ b`

• `a` and `b` are real numbers

• `u ≤ v`

• `u` and `v` are real vectors of the same dimension

• `A ≤ B`

• `A` and `B` are real matrices of the same size

• `t ≤ s`

• `t` and `s` are date or datetime structures

## Description

• If `a` and `b` are real numbers, then `a ≤ b` is `true` iff `a` is less than or equal to `b`. No epsilons are used. Hence, even if `a` and `b` are essentially equal, `a ≤ b` might be `false`. For example, `sin(π) ≤ 0` might or might not be `true`.

• If `u` and `v` are real vectors of the same dimension, then `u ≤ v` is `true` iff every component of `u` is less than or equal to the corresponding component of `v`. No epsilons are used.

• If `A` and `B` are real matrices of the same size, then `A ≤ B` is `true` iff every entry of `A` is less than or equal to the corresponding entry of `B`. No epsilons are used.

• If `t` and `s` are date or datetime structures, then `t ≤ s` is `true` iff `t` denotes the same or an earlier point in time than `s`.

The `≤` operator is implemented by the `LessThanOrEqualTo` function.

## Examples

`17/53 ≤ 73/220`
`true`
`❨❨6, 3, 1❩, ❨1, 0, 3❩❩ ≤ ❨❨10, 10, 10❩, ❨10, 10, 10❩❩`
`true`
`yesterday() ≤ today()`
`true`