There-exists sign

A mirrored capital E, the existential quantifier of formal logic.

Also known as: Existential quantifier, Backwards E

MathematicalScientificStandard profile

Meanings

∃ is the existential quantifier: it asserts that at least one member of a set satisfies a statement. Giuseppe Peano introduced it in 1897 as a reversed E, for the Latin existit.

Officially standardisedVerified fact
Is encoded as U+2203 THERE EXISTS in the Mathematical Operators block.
Contexts: Mathematics
Common modern usageVerified fact
Asserts that at least one member of the set being quantified over satisfies what follows, and is read 'there exists' or 'for some'.
Contexts: Mathematics
Common modern usageVerified fact
Was introduced by Giuseppe Peano in 1897 as a reversed capital E, for the Latin existit, three decades before the matching inverted A for universality.
Contexts: Mathematics
Common modern usageVerified fact
Is struck through to give ∄, 'there does not exist', one of the standard negations formed by a slash through a relation rather than by a separate symbol.
Contexts: Mathematics

Visual description

A capital Latin E reversed left to right: a vertical stroke on the right with three horizontal arms projecting to the left, at top, middle and foot.

Symmetry: horizontal
Orientation: mirrored

Used alongside: For-all sign
The two quantifiers of first-order logic, dual to one another.

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

Quantifier (logic)
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.
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.
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

Help improve this page

Meanings

∃ is the existential quantifier: it asserts that at least one member of a set satisfies a statement. Giuseppe Peano introduced it in 1897 as a reversed E, for the Latin existit.

Officially standardisedVerified fact

Is encoded as U+2203 THERE EXISTS in the Mathematical Operators block.

Contexts: Mathematics

Common modern usageVerified fact

Asserts that at least one member of the set being quantified over satisfies what follows, and is read 'there exists' or 'for some'.

Contexts: Mathematics

Common modern usageVerified fact

Was introduced by Giuseppe Peano in 1897 as a reversed capital E, for the Latin existit, three decades before the matching inverted A for universality.

Contexts: Mathematics

Common modern usageVerified fact

Is struck through to give ∄, 'there does not exist', one of the standard negations formed by a slash through a relation rather than by a separate symbol.

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

Quantifier (logic)
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.
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.
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