The Mathematical Symbol "Subset of or Equal To (⊆)"

The "Subset of or Equal To" Symbol (⊆)

The ⊆ symbol denotes a mathematical relationship where one set is either a subset of another set, or both sets are identical. Essentially, it signals that every element of the first set is also present in the second set or that both sets have the same elements.

Visual Representation

This symbol looks like the "less than" sign (`<`) combined with an underscore. This appearance corresponds to the idea of "less than or equal to", but in the context of sets rather than numbers.

Common Uses

The "Subset of or Equal To" relationship is fundamental in set theory and other mathematical disciplines:

  • Set Theory: In set theory, if set \( A \) is a subset of or is equivalent to set \( B \), it can be written as \( A ⊆ B \). This means all components of set \( A \) are also components of set \( B \).
  • Examples:
    • If set \( A = \{2, 3\} \) and set \( B = \{1, 2, 3, 4\} \), then \( A ⊆ B \) since all elements of \( A \) are contained in \( B \).
    • If set \( A = \{1, 2, 3\} \) and set \( B = \{1, 2, 3\} \), then \( A ⊆ B \) because \( A \) and \( B \) are identical.

Representation in Other Contexts

In LaTeX, which is a popular tool for typesetting mathematical and scientific documents, the "Subset of or Equal To" symbol can be represented with the `\subseteq` command when in a mathematical environment.

Conclusion

The ⊆ symbol is invaluable in set theory and numerous areas of mathematics for expressing the relationship where every element of one set is also an element of another set, or both sets are identical. Grasping this relationship is essential for understanding hierarchies and inclusion within sets.

Mathematical symbol 'Subset of or Equal To'

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Codes for the ⊆ Symbol

The Symbol⊆
Alt CodeAlt 8838
HTML Code&#8838;
HTML Entity&sube;
CSS Code\2286
Hex Code&#x2286;
UnicodeU+2286

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 8838. 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: &#8838;</b>My symbol: ⊆

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

HTML TextOutput
<b>My symbol: &sube;</b>My symbol: ⊆

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

CSS and HTML TextOutput
<style>
span:after {
content: "\2286";}
</style>
<span>My symbol:</span> 		My symbol: ⊆

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

HTML TextOutput
<b>My symbol: &#x2286;</b>My symbol: ⊆
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2286 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+2286. 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:
TypeOutput
2286
[Hold down Alt]
[Press x]		⊆
(The 2286 turns into ⊆. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u2286. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u2286"
document.write("My symbol: " + str)		My symbol: ⊆