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.


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.


  • 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.

Mathematical symbol 'Multiset Multiplication'

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Codes for the ⊍ Symbol

The Symbol
Alt CodeAlt 8845
HTML Code⊍
HTML Entity⊍
CSS Code\228D
Hex Code⊍

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 TextOutput
<b>My symbol: &#8845;</b>My symbol: ⊍

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

HTML TextOutput
<b>My symbol: &cupdot;</b>My symbol: ⊍

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

CSS and HTML TextOutput
span:after {
content: "\228D";}
<span>My symbol:</span>
My symbol: ⊍

(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).

HTML TextOutput
<b>My symbol: &#x228D;</b>My symbol: ⊍
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x228D to place the ⊍ symbol on your canvas. For example:
JavaScript Text
const x = "0x"+"E9"
ctx.fillText(String.fromCodePoint(x), 5, 5);

(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:
[Hold down Alt]
[Press x]

(The 228D turns into ⊍. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u228D. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u228D"
document.write("My symbol: " + str)
My symbol: ⊍