The Mathematical Symbol "Vertical Ellipsis (⋮)"
The ⋮ Symbol: Understanding the Vertical Ellipsis
In typography and mathematical notation, certain symbols carry with them a unique significance, often denoting continuation or omission. One such symbol is the ⋮, or the "Vertical Ellipsis". This article will offer insights into its usage and provide illustrative examples.
Usage
The ⋮ symbol serves as a vertical counterpart to the more common horizontal ellipsis (...). It is often used to denote the omission of elements in a vertical list or the continuation of a sequence. In mathematics, it frequently appears to suggest a pattern that extends downwards in matrices or series.
Examples
- Example 1: In matrices, the ⋮ symbol can indicate a continuation of elements. For instance, consider a 5x5 identity matrix. The top-left to bottom-right diagonal would have ones, and instead of writing out all five rows and columns, we might express the matrix as:
\[ \begin{bmatrix} 1 & 0 & \dots \\ 0 & 1 & \dots \\ ⋮ & ⋮ \\ 0 & 0 & 1 \end{bmatrix} \]
The ⋮ here indicates the pattern continues in the specified direction. - Example 2: In sequences or series, the ⋮ can denote the continuation of a pattern. Given the sequence:
\( a_1, a_2, a_3, ⋮, a_n \)
The vertical ellipsis indicates the sequence continues in the described manner up to \( a_n \).
To sum up, the ⋮ symbol, or vertical ellipsis, plays an indispensable role in various notational contexts. Whether indicating omitted items or suggesting a continuation, it aids in succinctly conveying patterns and sequences without the need for exhaustive detailing.
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Codes for the ⋮ Symbol
| The Symbol | ⋮ | |
| Alt Code | Alt 8942 | |
| HTML Code | ⋮ | |
| HTML Entity | ⋮ | |
| CSS Code | \22EE | |
| Hex Code | ⋮ | |
| Unicode | U+22EE |
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 8942. 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: "\22EE";} </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: ⋮ |
| 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+22EE. 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 |
|---|---|
| 22EE [Hold down Alt] [Press x] | ⋮ (The 22EE turns into ⋮. Note that you can omit any leading zeros.) |
| JavaScript Text | Output |
|---|---|
| let str = "\u22EE" document.write("My symbol: " + str) | My symbol: ⋮ |