The Mathematical Symbol "Midline Horizontal Ellipsis (⋯)"
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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 | ⋯ | |
| Alt Code | Alt 8943 | |
| HTML Code | ⋯ | |
| HTML Entity | ⋯ | |
| CSS Code | \22EF | |
| Hex Code | ⋯ | |
| Unicode | U+22EF |
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: ⋯</b> | My symbol: ⋯ |
(Method 4) Use the HTML Entity Code (for webpages).
| HTML Text | Output |
|---|---|
| <b>My symbol: ⋯</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: ⋯</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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More about Mathematical Symbols
Mathematics is a universal language that is used to describe and understand the intricacies of the universe. At the heart of this language are symbols, concise representations that convey specific meanings and ideas.
Just as letters come together to form words in spoken languages, mathematical symbols combine to form expressions and equations, encapsulating intricate ideas in a compact form. The history of these symbols is as varied as their meanings; some have been in use for centuries while others have been introduced more recently to describe new discoveries and concepts. Whether you are a student, educator, researcher, or simply curious, this list of mathematical symbols will serve as a guide, shedding light on their meanings, origins, and applications.
From the simple plus and minus signs to the more esoteric and complex, each symbol has its unique story and significance.
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Full List of Mathematical Symbols
