Intersection sign

An inverted rounded U, denoting what two sets have in common.

Also known as: Cap, Upside-down U, Arch shape

MathematicalScientificStandard profile

Meanings

∩ denotes the intersection of two sets: everything belonging to both. It is the union sign turned upside down, and the two are among the most frequently reversed symbols in mathematics.

Officially standardisedVerified fact
Is encoded as U+2229 INTERSECTION in the Mathematical Operators block.
Contexts: Mathematics
Common modern usageVerified fact
Denotes the set of everything belonging to both of the two sets it joins.
Contexts: Mathematics
Common modern usageVerified fact
Is read aloud as 'cap', paired with 'cup' for the union sign — a naming convention that exists because the shapes alone are so easily reversed.
Contexts: Mathematics

Visual description

A single stroke rising, curving across the top and descending again, forming an open-bottomed arch with legs of equal length.

Symmetry: vertical
Orientation: inverted

Commonly confused with: Union sign
Vertical reflection is the entire difference between them.
Opposite of: Union sign
Everything in both sets, against everything in either.

Compare: Intersection (∩) vs union (∪) →

Confidence

IdentityHigh confidence: High confidence because the identity is defined by a current official standard, but multiple independent sources agree.
Historical originModerate confidence: Moderate confidence because the historical origin is documented in encyclopedic references, but multiple independent sources agree, but early or supporting evidence is limited, but the regional or cultural match to this specific claim is not precise.
Current useHigh confidence: High confidence because the current use is defined by a current official standard, but multiple independent sources agree.
Visual matchHigh confidence: High confidence because the visual match is documented in encyclopedic references, but multiple independent sources agree.

Sources

Glossary of mathematical symbols
Wikipedia · retrieved 2026-07-31
Tertiary reference. Used for what the notation means in ordinary mathematical practice and for attribution of its introduction, not for a claim that any body defines it.
Set (mathematics)
Wikipedia · retrieved 2026-07-31
Tertiary reference. Used for what the notation means in ordinary mathematical practice and for attribution of its introduction, not for a claim that any body defines it.
Unicode Code Chart: Mathematical Operators (U+2200–U+22FF)
The Unicode Consortium · retrieved 2026-07-30
Authoritative for the character's code point, name and block only. Unicode assigns identity; it does not define what a symbol means in use.

Last reviewed 2026-08-01

Part of

Set theory and logic notation

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Meanings

∩ denotes the intersection of two sets: everything belonging to both. It is the union sign turned upside down, and the two are among the most frequently reversed symbols in mathematics.

Officially standardisedVerified fact

Is encoded as U+2229 INTERSECTION in the Mathematical Operators block.

Contexts: Mathematics

Common modern usageVerified fact

Denotes the set of everything belonging to both of the two sets it joins.

Contexts: Mathematics

Common modern usageVerified fact

Is read aloud as 'cap', paired with 'cup' for the union sign — a naming convention that exists because the shapes alone are so easily reversed.

Contexts: Mathematics

Confidence

IdentityHigh confidence: High confidence because the identity is defined by a current official standard, but multiple independent sources agree.
Historical originModerate confidence: Moderate confidence because the historical origin is documented in encyclopedic references, but multiple independent sources agree, but early or supporting evidence is limited, but the regional or cultural match to this specific claim is not precise.
Current useHigh confidence: High confidence because the current use is defined by a current official standard, but multiple independent sources agree.
Visual matchHigh confidence: High confidence because the visual match is documented in encyclopedic references, but multiple independent sources agree.

Sources

Glossary of mathematical symbols
Wikipedia · retrieved 2026-07-31
Tertiary reference. Used for what the notation means in ordinary mathematical practice and for attribution of its introduction, not for a claim that any body defines it.
Set (mathematics)
Wikipedia · retrieved 2026-07-31
Tertiary reference. Used for what the notation means in ordinary mathematical practice and for attribution of its introduction, not for a claim that any body defines it.
Unicode Code Chart: Mathematical Operators (U+2200–U+22FF)
The Unicode Consortium · retrieved 2026-07-30
Authoritative for the character's code point, name and block only. Unicode assigns identity; it does not define what a symbol means in use.

Last reviewed 2026-08-01

Meanings

Visual description

Related & commonly confused symbols

Meanings

Visual description

Related & commonly confused symbols