The Mathematical Symbol "Does Not Contain As Member (∌)"

Understanding the "Does Not Contain As Member" Symbol (∌): A Set Theory Perspective

Mathematics is enriched with symbols that convey specific meanings and relationships. Within the realm of set theory, the symbol for "Does Not Contain As Member", depicted as ∌, plays an instrumental role.

Decoding the ∌ Symbol

Set theory deals with the study of sets, which are collections of objects. The ∌ symbol, at its core, represents a specific relationship between an element and a set. When an element is said to "not be a member of" a particular set, the ∌ notation is employed.

Example 1:

Let's consider a set \( S \) defined as the set of all even integers. If we want to indicate that the number 3 is not a member of this set, the relationship can be conveyed as:

3 ∌ \( S \)

Example 2:

Suppose we have a set \( T \) representing the primary colors, defined as \( T = \{\text{"red"}, \text{"blue"}, \text{"yellow"}\} \). If we wish to express that "green" is not a member of this set, the notation would be:

"green" ∌ \( T \)

It's crucial to differentiate between the ∌ symbol and its counterpart which indicates membership (∈). While ∈ confirms an element's presence in a set, ∌ explicitly denotes its absence. This distinction is foundational in set theory and helps in formulating and understanding various mathematical and logical assertions.

Mathematical symbol 'Does Not Contain As Member'

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Codes for the ∌ Symbol

The Symbol
Alt CodeAlt 8716
HTML Code∌
HTML Entity∌
CSS Code\220C
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 8716. 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: &#8716;</b>My symbol: ∌

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

HTML TextOutput
<b>My symbol: &notni;</b>My symbol: ∌

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

CSS and HTML TextOutput
span:after {
content: "\220C";}
<span>My symbol:</span>
My symbol: ∌

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

HTML TextOutput
<b>My symbol: &#x220C;</b>My symbol: ∌
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x220C 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+220C. 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 220C turns into ∌. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u220C. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u220C"
document.write("My symbol: " + str)
My symbol: ∌