# Ordinal Data - Comparison Operator (Order, Equality)

Comparison Operator

All comparison operators have the same priority, which is lower than that of all numerical operators.

A comparison operator test the order relationship between two operands and returns a Boolean.

The result of a comparison is a Boolean

Comparison Operator are tiddly coupled with the order and equivalence notion in order to sort data.

## 3 - Chain

Comparisons may be chained.

For example, `a < b == c` tests whether:

• `a < b`
• and moreover `b == c`

## 4 - Relation

Comparison operator models two kind of relation:

• Order Relation
• and Equivalence Relation

Binary relation are used in many branches of mathematics to model this relation. See Data Modeling - Binary Relation.

### 4.1 - Order relation

Order relation, including strict orders:

• greater than
• greater than or equal to
• less than
• less than or equal to
• divides (evenly)
• is a subset of

### 4.2 - Equivalence relation

• equality
• is parallel to (for affine spaces)
• is in bijection with
• isomorphy

## 5 - Combination

Comparisons may be combined using the Boolean operators `and` and `or`.

## 6 - List

### 6.1 - Order

Operation Description
< strictly less than
<= less than or equal
> strictly greater than
>= greater than or equal
in check whether a value occurs in a list
not in check whether a value does not occur in a list