There exists symbol (∃)
∃ means “there exists” or “there is”. It is the existential quantifier: ∃x P(x) says that P(x) is true of at least one x.
Easily confused with
How to read it
Oscar Levin’s Discrete Mathematics reads ∃ as “there exists” or “there is”: ∃x (x < 0) asserts that there is a number less than 0. One is enough; ∃ doesn’t say how many. The Stanford Encyclopedia of Philosophy reads ∃v θ as “there is a v such that θ”. Like ∀, it is always followed by a variable (forall x: Calgary). The two are linked through negation: Levin gives ¬∃x P(x), “nothing is P”, as equivalent to ∀x ¬P(x), “everything is not P”. Unicode names the character THERE EXISTS (U+2203) and has a separate crossed-out form, ∄ (U+2204), “there does not exist”.
Also searched as: ∃, ∄, backwards E, existential quantifier, there does not exist, there is symbol.
Look-alikes
∃ is a capital E turned round, as ∀ is a capital A upside down; forall x: Calgary describes them as a rotated E and a rotated A. The element-of sign ∈, which began as a Greek epsilon, is a different symbol.
Read next
- Next in Logic symbolsTurnstile (⊢)⊢, the turnstile, means “proves” or “derives”. Γ ⊢ φ says that φ can be proved from the premises Γ using the rules of a proof system.
- The same shape in Smoke and CO alarm soundsLow-frequency 520 Hz alarm (sleeping rooms)A fire alarm in a sleeping room that sounds a low buzz in place of a high-pitched beep. It is the three-beep fire alarm rhythm at 520 Hz, which NFPA 72 requires of alarms provided to wake people in sleeping areas.
More logic symbols
The same shape elsewhere
Browse symbols drawn with letters and numbers or lines.
Sources
- Discrete Mathematics, 0.2 Mathematical Statements, Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd edition, Oscar Levin, University of Northern Colorado (Open Math Books), Universal and existential quantifiers
- forall x: Calgary. An Introduction to Formal Logic, P. D. Magnus, Tim Button, Robert Trueman and Richard Zach, forall x: Calgary (Fall 2025 edition), Open Logic Project, University of Calgary, Sec. 23.2 Quantifiers; Appendix A.2 Alternative symbols
- Classical Logic, Stewart Shapiro and Teresa Kouri Kissel, Stanford Encyclopedia of Philosophy, Metaphysics Research Lab, Stanford University, Sec. 2.3 Compound formulas
- Earliest Uses of Symbols of Set Theory and Logic, Jeff Miller, Earliest Uses of Various Mathematical Symbols, MacTutor History of Mathematics, University of St Andrews, Existence (existential quantifier)
- Mathematical Operators: Range 2200–22FF (code chart), The Unicode Standard, Version 18.0, Unicode Consortium, Miscellaneous mathematical symbols, 2203–2204
Researched, edited and approved by Rory Hansen before publishing. Last reviewed October 9, 2026. How we research
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