Sets and Set Operations

Q

How to represent sets and set operations in MathML?

✍: FYIcenter.com

A

"ISO 80000-2 Quantities and Units - Mathematics" specifies that sets and set operations should be represented as described below:

Set Identifier - A capital letter in italic style should be used as the identifier for a generic set. For example: A or B.

Set Element - A lowercase letter in italic style should be used as the identifier for an element in a set. For example: x or y.

List of Elements - A set can be defined as a list of its elements enclosed in curly brackets: {x1, x2, x3, …}.

Empty Set - An empty set should be identified by the Empty Set symbol, ∅ (U+2205, ∅ or ∅).

Element-Of Relation - The element-of relation states that the first operand is an element of the second operand. The operator should be expressed with the Element-Of symbol, ∈ (U+2208, ∈ or &element;). For example, x ∈ A.

Not-An-Element-Of Relation - The not-an-element-of relation states that the first operand is not an element of the second operand. The operator should be expressed with the Not-An-Element-Of symbol, ∉ (U+2209, ∉ or ∉). For example, x ∉ A.

Such-That Condition - The such-that condition should be represented by the Vertical Bar symbol, | (U+007C or |). For example, {x ∈ ℤ | x ≥ 0}.

Union of Sets - The union of two sets should be represented by the Union symbol ∪ (U+222A,∪ or ∪). For example, A ∪ A ≝ {x ∈ A ∨ x ∈ B}.

Intersection of Sets - The intersection of two sets should be represented by the Intersection symbol ∩ (U+2229,∩ or ∩). For example, A ∩ A ≝ {x ∈ A ∧ x ∈ B}.

 

⇒ Sets of Numbers

⇐ Logical Values and Operator Symbols

⇑ ISO 80000-2 Quantities and Units - Mathematics

⇑⇑ MathML (Mathematical Markup Language)

2026-10-17, ∼1742🔥, 0💬