Midline Horizontal Ellipsis

The Mathematical Symbol "Midline Horizontal Ellipsis (⋯)"

The ⋯ Symbol in Mathematics: Midline Horizontal Ellipsis

The diverse array of symbols in mathematics often provides concise ways to represent complex ideas or sequences. Among these symbols is the ⋯, known as the "Midline Horizontal Ellipsis". This article aims to shed light on the primary applications and significance of the ⋯ symbol, complemented by relevant examples.

Usage

The ⋯ symbol primarily indicates the continuation of a certain pattern or sequence in mathematics. When placed horizontally at the middle height of a line, it denotes that the sequence or pattern being presented can be continued in the manner established by the given context.

Examples

• Example 1: Representing Sequences: When illustrating a sequence of numbers where the pattern is clear but listing every term would be cumbersome, the ⋯ symbol can be employed. For instance:
  1, 2, 3, ⋯, n
  This notation suggests a sequence that starts with 1 and goes up to an arbitrary number n.
• Example 2: In Algebraic Expressions: For polynomials or other algebraic structures where a specific pattern is present but not all terms are explicitly mentioned, the ⋯ can be useful. Consider:
  \( a_1x + a_2x^2 + a_3x^3 + ⋯ + a_nx^n \)
  Here, the ⋯ indicates the continuation of the polynomial terms up to the nth term.

In summary, the ⋯ symbol serves as a valuable tool in mathematical notation to signify the continuation of a clear and understood pattern. Its utility ensures concise representation without sacrificing clarity or meaning.

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Codes for the ⋯ Symbol

The Symbol	⋯	copy
Alt Code	Alt 8943	copy
HTML Code	⋯	copy
HTML Entity	⋯	copy
CSS Code	\22EF	copy
Hex Code	⋯	copy
Unicode	U+22EF	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 8943. 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: &#8943;</b>	My symbol: ⋯

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

HTML Text	Output
<b>My symbol: &ctdot;</b>	My symbol: ⋯

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

CSS and HTML Text	Output
<style> span:after { content: "\22EF";} </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: &#x22EF;</b>	My symbol: ⋯

On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x22EF 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+22EF. 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
22EF [Hold down Alt] [Press x]	⋯ (The 22EF turns into ⋯. Note that you can omit any leading zeros.)

In JavaScript, the syntax is \uXXXX. So, our example would be \u22EF. (Note that the format is 4 hexadecimal characters.)

JavaScript Text	Output
let str = "\u22EF" document.write("My symbol: " + str)	My symbol: ⋯

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