The Mathematical Symbol "Double Subset (⋐)"

The Double Subset (⋐): An Introduction

The Double Subset, represented as ⋐ is a mathematical notation often used in set theory. This symbol represents a concept wherein one set is not only a subset of another but is also possibly equal to it. In this article, we will explore the primary use of the Double Subset symbol with two illustrative examples.

Usage in Set Theory

In set theory, the ⋐ notation is used to denote that one set, say A, is a subset of another set, B, or is equal to B. It encapsulates both the notions of strict subset and non-strict subset.

Example 1:

If we have two sets:

A = {1, 2, 3} and B = {1, 2, 3, 4, 5}

We can rightly say that A ⋐ B, since every element of A is also an element of B.

Example 2:

For the sets:

X = {a, b, c} and Y = {a, b, c}

We can state that X ⋐ Y, since X and Y contain the same elements. Here, the notation also implies X = Y.

These examples demonstrate the versatility of the Double Subset notation in representing relationships between sets. It's essential to understand the context in which it's used, as it can convey different subset relationships based on the given sets.

Mathematical symbol 'Double Subset'

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Codes for the ⋐ Symbol

The Symbol
Alt CodeAlt 8912
HTML Code⋐
HTML Entity⋐
CSS Code\22D0
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 8912. 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: &#8912;</b>My symbol: ⋐

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

HTML TextOutput
<b>My symbol: &Sub;</b>My symbol: ⋐

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

CSS and HTML TextOutput
span:after {
content: "\22D0";}
<span>My symbol:</span>
My symbol: ⋐

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

HTML TextOutput
<b>My symbol: &#x22D0;</b>My symbol: ⋐
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x22D0 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+22D0. 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 22D0 turns into ⋐. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u22D0. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u22D0"
document.write("My symbol: " + str)
My symbol: ⋐