The Mathematical Symbol "Multiset Multiplication (⊍)"
The ⊍ Symbol in Mathematics: Multiset Multiplication
In the vast landscape of mathematical symbols, each serves a unique purpose. The ⊍ symbol, denoting "Multiset Multiplication", is a particularly intriguing one. This article delves into its use and significance, supplemented by illustrative examples.
Usage
The ⊍ symbol is utilized to represent the multiplication of multisets. Multisets differ from traditional sets as they allow multiple occurrences of elements. The ⊍ symbol can be visualized as combining the repeated instances of elements from both multisets in a multiplicative manner.
Examples
- Example 1: Consider two multisets A = {2,2,3} and B = {2,3,3}. Their multiset multiplication is represented as:
A ⊍ B = {4,4,6,6,6,9}
Here, the ⊍ symbol has multiplied each element from A with every element from B. - Example 2: For multisets X = {a,a,b} and Y = {a,b,b}, the multiset multiplication is:
X ⊍ Y = \({a^2, a^2, ab, ab, ab, b^2, b^2, ab, ab, b^2}\)
The ⊍ operation has effectively represented all multiplicative combinations of the elements from X and Y.
To conclude, the ⊍ symbol offers a specialized representation for the multiplication of multisets. Its unique operation captures the combinatorial essence of multiplying each element in one multiset by each element in another, a task not captured by traditional set operations.
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Codes for the ⊍ Symbol
| The Symbol | ⊍ | |
| Alt Code | Alt 8845 | |
| HTML Code | ⊍ | |
| HTML Entity | ⊍ | |
| CSS Code | \228D | |
| Hex Code | ⊍ | |
| Unicode | U+228D |
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 8845. 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: "\228D";} </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+228D. 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 |
|---|---|
| 228D [Hold down Alt] [Press x] | ⊍ (The 228D turns into ⊍. Note that you can omit any leading zeros.) |
| JavaScript Text | Output |
|---|---|
| let str = "\u228D" document.write("My symbol: " + str) | My symbol: ⊍ |