The Mathematical Symbol "Intersection (∩)"

The ∩ Symbol in Mathematics: Intersection

In the rich tapestry of mathematical symbols, the ∩ or "Intersection" symbol occupies a foundational position, especially within set theory. This article will explore its significance, primary applications, and provide a couple of illustrative examples for clarity.

Usage

The ∩ symbol is chiefly used in set theory to denote the intersection of two sets. The intersection of two sets contains all elements that are present in both sets. If an element belongs to both Set A and Set B, then it will belong to the intersection of A and B.

Examples

  • Example 1: Basic intersection:
    Let Set A = {1, 2, 3, 4} and Set B = {3, 4, 5, 6}. The intersection of Sets A and B, represented as \( A ∩ B \), is the set {3, 4} because these two numbers appear in both sets.
  • Example 2: Intersection with no common elements:
    If Set C = {7, 8, 9} and Set D = {10, 11, 12}, then \( C ∩ D \) is the empty set, usually denoted by {}. This is because there are no common elements between Sets C and D.

In summary, the ∩ symbol provides a succinct way to represent the common elements between two sets. A thorough understanding of its usage is paramount for anyone delving into set theory and its applications in various mathematical domains.

Mathematical symbol 'Intersection'

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Codes for the ∩ Symbol

The Symbol∩
Alt CodeAlt 8745
HTML Code∩
HTML Entity∩
CSS Code\2229
Hex Code∩
UnicodeU+2229

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 8745. 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: &#8745;</b>My symbol: ∩

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

HTML TextOutput
<b>My symbol: &cap;</b>My symbol: ∩

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

CSS and HTML TextOutput
<style>
span:after {
content: "\2229";}
</style>
<span>My symbol:</span> 		My symbol: ∩

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

HTML TextOutput
<b>My symbol: &#x2229;</b>My symbol: ∩
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2229 to place the ∩ symbol on your canvas. For example:
JavaScript Text
const x = "0x"+"E9"
ctx.fillText(String.fromCodePoint(x), 5, 5);
Output

∩

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

The Unicode for ∩ is U+2229. 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:
TypeOutput
2229
[Hold down Alt]
[Press x]		∩
(The 2229 turns into ∩. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u2229. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u2229"
document.write("My symbol: " + str)		My symbol: ∩