Empty Set

The Mathematical Symbol "Empty Set (∅)"

The ∅ Symbol in Mathematics: Empty Set

In the intricate world of mathematical symbols, the ∅ symbol stands out due to its simple yet profound concept. Representing the "Empty Set", it denotes a set with no elements. This article provides a closer look at this fundamental concept and its applications in mathematics.

Usage

The ∅ symbol is used to represent a set that has no members or elements. In set theory, an essential branch of mathematical logic and foundational mathematics, the concept of the empty set plays a crucial role as it provides a basis for building other sets.

Examples

• Example 1: Representing an empty set can be straightforward:
  \( S = ∅ \)
  This notation signifies that set \( S \) contains no elements.
• Example 2: When considering the intersection of two disjoint sets, the result can be the empty set:
  Let \( A = \{1, 2\} \) and \( B = \{3, 4\} \), then \( A \cap B = ∅ \)
  This indicates that there are no common elements between sets \( A \) and \( B \).

In summary, the ∅ symbol offers a concise and universal representation for the concept of 'nothingness' in the context of set theory. Recognizing its importance, mathematicians use this symbol to describe situations where a set has no members, emphasizing its foundational role in the mathematics of sets.

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Codes for the ∅ Symbol

The Symbol	∅	copy
Alt Code	Alt 8709	copy
HTML Code	∅	copy
HTML Entity	∅	copy
CSS Code	\2205	copy
Hex Code	∅	copy
Unicode	U+2205	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 8709. 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: &#8709;</b>	My symbol: ∅

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

HTML Text	Output
<b>My symbol: &empty;</b>	My symbol: ∅

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

CSS and HTML Text	Output
<style> span:after { content: "\2205";} </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: &#x2205;</b>	My symbol: ∅

On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2205 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+2205. 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
2205 [Hold down Alt] [Press x]	∅ (The 2205 turns into ∅. Note that you can omit any leading zeros.)

In JavaScript, the syntax is \uXXXX. So, our example would be \u2205. (Note that the format is 4 hexadecimal characters.)

JavaScript Text	Output
let str = "\u2205" document.write("My symbol: " + str)	My symbol: ∅

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