The Mathematical Symbol "There Exists (∃)"

The ∃ Symbol in Logic: "There Exists"

The ∃ symbol, read as "there exists", is a fundamental notation in mathematical logic and set theory. It expresses existential quantification, a core concept signifying that within a particular domain, there is at least one element satisfying a certain property or condition. In this article, we'll delve into its interpretation and present two illustrative examples.


In logic and mathematics, the ∃ symbol is used to convey the presence of at least one element that fulfills a given criterion. When combined with a variable and a proposition, it asserts the existence of an instance where the proposition holds true for that variable.


  • Example 1: Mathematical Statement:
    If we wish to state that there exists a real number \( x \) such that \( x^2 = 4 \), it can be written as:
    ∃ \( x \) in ℝ : \( x^2 = 4 \). In this example, the numbers 2 and -2 are the real numbers satisfying the equation.
  • Example 2: Set Theory:
    To claim that a set \( S \) has at least one odd number, one can write:
    ∃ \( n \) in \( S \) : \( n \) is odd. This statement verifies the presence of at least one odd number within the set \( S \).

In summary, the ∃ symbol is pivotal in mathematical expressions, allowing mathematicians to assert the existence of elements with specific properties within a defined domain. It stands as a testament to the precision and specificity inherent to mathematical language.

Mathematical symbol 'There Exists'

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Codes for the ∃ Symbol

The Symbol
Alt CodeAlt 8707
HTML Code∃
HTML Entity∃
CSS Code\2203
Hex Code∃

How To Insert the ∃ Symbol

(Method 1) Copy and paste the symbol.

The easiest way to get the ∃ symbol is to copy and paste it into your document.

Bear in mind that this is a UTF-8 encoded character. It must be encoded as UTF-8 at all stages (copying, replacing, editing, pasting), otherwise it will render as random characters or the dreaded �.

(Method 2) Use the "Alt Code."

If you have a keyboard with a numeric pad, you can use this method. Simply hold down the Alt key and type 8707. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

(Method 3) Use the HTML Decimal Code (for webpages).

HTML TextOutput
<b>My symbol: &#8707;</b>My symbol: ∃

(Method 4) Use the HTML Entity Code (for webpages).

HTML TextOutput
<b>My symbol: &exist;</b>My symbol: ∃

(Method 5) Use the CSS Code (for webpages).

CSS and HTML TextOutput
span:after {
content: "\2203";}
<span>My symbol:</span>
My symbol: ∃

(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).

HTML TextOutput
<b>My symbol: &#x2203;</b>My symbol: ∃
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2203 to place the ∃ symbol on your canvas. For example:
JavaScript Text
const x = "0x"+"E9"
ctx.fillText(String.fromCodePoint(x), 5, 5);

(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).

The Unicode for ∃ is U+2203. The important part is the hexadecimal number after the U+, which is used in various formats. For example, in Microsoft Office applications (e.g. Word, PowerPoint), do the following:
[Hold down Alt]
[Press x]

(The 2203 turns into ∃. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u2203. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u2203"
document.write("My symbol: " + str)
My symbol: ∃