The Mathematical Symbol "Neither a Subset of nor Equal To (⊈)"

Deciphering the "Neither a Subset of nor Equal To" Symbol (⊈)

Mathematics is a discipline that thrives on precision, and this precision is often facilitated by its diverse array of symbols. One such intriguing symbol is ⊈, which stands for "Neither a Subset of nor Equal To". This article delves into its meaning, applications, and relevance in mathematical contexts.

Interpreting ⊈

The ⊈ symbol is used in set theory to denote that one set is neither a subset of nor equal to another set. It clarifies that the set on the left does not contain all the elements of the set on the right, nor are the two sets identical.

Example 1: Basic Set Relationship

If \( A \) and \( B \) are two sets and \( A \) does not contain all the elements of \( B \) nor is identical to \( B \), the relationship can be expressed as: \[ A ⊈ B \]

Example 2: Working with Specific Sets

Suppose we have two sets, \( A = \{1, 2\} \) and \( B = \{1, 2, 3\} \). Since \( A \) doesn't contain all the elements of \( B \) and isn't identical to \( B \), we can denote: \[ A ⊈ B \]

Where is ⊈ Used?

The ⊈ notation is specifically tied to set theory and its applications:

  • Mathematical Logic: In describing relationships between different sets.
  • Computer Science: When working with data structures like sets and subsets.
  • Probability Theory: In discussing sample spaces and event spaces.

It serves as a clear and concise way to depict a specific non-inclusive relationship between two sets, making it easier to decipher and work with complex set relationships.

In summary, the ⊈ symbol, synonymous with "Neither a Subset of nor Equal To", is a testament to the nuance and specificity inherent in mathematical notation. It plays a critical role in ensuring clarity, especially in domains where set relationships are paramount.

Mathematical symbol 'Neither a Subset of nor Equal To'

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Codes for the ⊈ Symbol

The Symbol
Alt CodeAlt 8840
HTML Code⊈
HTML Entity⊈
CSS Code\2288
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 8840. 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: &#8840;</b>My symbol: ⊈

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

HTML TextOutput
<b>My symbol: &nsube;</b>My symbol: ⊈

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

CSS and HTML TextOutput
span:after {
content: "\2288";}
<span>My symbol:</span>
My symbol: ⊈

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

HTML TextOutput
<b>My symbol: &#x2288;</b>My symbol: ⊈
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2288 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+2288. 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 2288 turns into ⊈. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u2288. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u2288"
document.write("My symbol: " + str)
My symbol: ⊈