∃ There Exists Symbol
The there-exists sign (∃) is the existential quantifier — “there is at least one”. It is a backwards E, and its own character, not a rotated letter.
Also known as: there exists, there exists symbol, there exist symbol, there exists math symbol, there exists symbol latex, existential quantifier symbol, backwards e.
Codes
| Symbol | ∃ | |
| There does not exist | ∄ · U+2204 | |
| For all | ∀ · U+2200 | |
| Unicode | U+2203 | |
| HTML entity (named) | ∃ | |
| HTML entity (decimal) | ∃ | |
| HTML entity (hex) | ∃ | |
| CSS | \2203 | |
| LaTeX | \exists | |
| Windows Alt code | Alt + 8707 |
How to type ∃ (There Exists Symbol)
Alt + 8707 works in apps that accept decimal-Unicode Alt input. In Word type 2203 then Alt + X; elsewhere press Win + . (period) and search “there exists”.
No default keystroke. Open Character Viewer (Control + Cmd + Space) and search “there exists”, or copy ∃ above.
Type 2203, then press Alt + X to convert it to ∃ (2204 then Alt + X gives ∄).
Insert → Special characters, then search “there exists” — or inside an Equation type \exists.
Use \exists in math mode; \nexists gives ∄, and \exists! is the conventional way to write “there exists exactly one”.
Usage
- ∃x P(x) reads “there exists an x such that P(x)” — at least one, possibly many.
- ∃ and ∀ are duals: ¬∃x P(x) is the same claim as ∀x ¬P(x) — “nothing satisfies P” equals “everything fails P”. Getting this negation right is most of what quantifier exercises test.
- Order matters and is the classic exam trap. ∀x ∃y (y > x) is true over the reals — for every number there is a bigger one. ∃y ∀x (y > x) is false — it claims one number beats them all. Same symbols, opposite meaning.
- ∃! means “there exists exactly one” (unique existence). There is no single Unicode character for it; it is written as ∃ followed by an exclamation mark.
- Do not fake it with a rotated E or the Cyrillic Э (U+042D). ∃ (U+2203) is its own character — the lookalikes will not search, sort or typeset as a quantifier.