## The Mathematical Symbol "Not Tilde (≁)"

The "Not Tilde" Symbol (≁): An Expression of Non-Equivalence

Mathematical notation has a myriad of symbols to express relationships between quantities, operations, and objects. Among these symbols, the ≁ or "Not Tilde" holds a particular importance when highlighting non-equivalence or dissimilarity between entities. This article explores the depth, significance, and applications of ≁.

## Decoding the ≁ Symbol

The ≁ symbol fundamentally denotes that two entities are not similar to or not equivalent. It is the negation of the tilde (~), which usually represents similarity or approximation.

Example 1: Mathematical Relations

Let's consider two functions $$f(x)$$ and $$g(x)$$. If they are not approximately equivalent, we can express this as: $$f(x) ≁ g(x)$$.

Example 2: Expressing Dissimilarity

If we have two vectors $$\mathbf{A}$$ and $$\mathbf{B}$$ that are not similar in some defined manner, it can be articulated as: $$\mathbf{A} ≁ \mathbf{B}$$.

## Domains of ≁ Application

The ≁ symbol finds usage across various mathematical disciplines:

• Algebra: To indicate that two algebraic structures are not isomorphic or similar.
• Analysis: Demonstrating that two functions are not approximately equivalent.
• Vector Spaces: To denote non-similarity between vectors or matrices.

While the ≁ symbol often stands as an indicator of non-equivalence, it's essential to be context-aware. Depending on the mathematical context, its specific interpretation might vary, but its central theme revolves around a lack of similarity or approximation.

In summary, the ≁ symbol serves as an indispensable tool in mathematics to indicate non-equivalence or dissimilarity. Its presence ensures that mathematical expressions are accurate, succinct, and free from ambiguity, making it an integral part of the mathematical lexicon.

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## Codes for the ≁ Symbol

 The Symbol ≁ Alt Code Alt 8769 HTML Code ≁ HTML Entity ≁ CSS Code \2241 Hex Code ≁ Unicode U+2241

## 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 8769. 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: &#8769;</b>My symbol: ≁

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

HTML TextOutput
<b>My symbol: &nsim;</b>My symbol: ≁

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

CSS and HTML TextOutput
<style>
span:after {
content: "\2241";}
</style>
<span>My symbol:</span>
My symbol: ≁

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

HTML TextOutput
<b>My symbol: &#x2241;</b>My symbol: ≁
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2241 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+2241. 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
2241
[Hold down Alt]
[Press x]

(The 2241 turns into ≁. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u2241. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u2241"
document.write("My symbol: " + str)
My symbol: ≁