Complement

The Mathematical Symbol "Complement (∁)"

The ∁ Symbol in Mathematics: Complement

Mathematics is replete with symbols, each encapsulating a unique concept. The ∁ symbol, known as "Complement", is a vital notation predominantly used in set theory. This article delineates its usage and illustrates with examples for a clearer understanding.

Usage

The ∁ symbol represents the complement of a set in set theory. Essentially, the complement of a set \( A \) with respect to a universal set \( U \) consists of all the elements in \( U \) that are not in \( A \).

Examples

• Example 1: Basic set complement:
  Given a universal set \( U = \{1, 2, 3, 4, 5\} \) and a subset \( A = \{1, 2\} \),
  The complement of \( A \) in \( U \) is:
  \( A∁ = \{3, 4, 5\} \)
• Example 2: Complement of an empty set:
  Given a universal set \( U = \{a, b, c\} \) and an empty set \( \emptyset \),
  The complement of \( \emptyset \) in \( U \) is:
  \( \emptyset∁ = \{a, b, c\} \)

In summary, the ∁ symbol offers a concise means to express the idea of "everything outside of" a particular set in the context of a universal set. Grasping its concept is instrumental in understanding various operations and properties in set theory.

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Codes for the ∁ Symbol

The Symbol	∁	copy
Alt Code	Alt 8705	copy
HTML Code	∁	copy
HTML Entity	∁	copy
CSS Code	\2201	copy
Hex Code	∁	copy
Unicode	U+2201	copy

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 8705. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

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

HTML Text	Output
<b>My symbol: &#8705;</b>	My symbol: ∁

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

HTML Text	Output
<b>My symbol: &comp;</b>	My symbol: ∁

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

CSS and HTML Text	Output
<style> span:after { content: "\2201";} </style> <span>My symbol:</span>	My symbol: ∁

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

HTML Text	Output
<b>My symbol: &#x2201;</b>	My symbol: ∁

On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2201 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+2201. 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:

Type	Output
2201 [Hold down Alt] [Press x]	∁ (The 2201 turns into ∁. Note that you can omit any leading zeros.)

In JavaScript, the syntax is \uXXXX. So, our example would be \u2201. (Note that the format is 4 hexadecimal characters.)

JavaScript Text	Output
let str = "\u2201" document.write("My symbol: " + str)	My symbol: ∁

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