The Mathematical Symbol "Does Not Succeed (⊁)"

The "Does Not Succeed" Symbol (⊁): Insights and Applications

Throughout mathematical notation, symbols often represent complex relationships and comparisons. One such symbol is the "Does Not Succeed" notation, depicted as ⊁. This article aims to shed light on the meaning and use of this symbol with a couple of illustrative examples.

Understanding ⊁

The ⊁ symbol is fundamentally a relational symbol that expresses a specific type of inequality. When used between two entities, it asserts that the first entity does not succeed, or is not greater than, the second entity. However, it doesn't confirm that the first is less than or equal to the second — only that it isn't greater.

Example 1:

In the domain of real numbers, if we have two numbers \( a \) and \( b \) and we want to specify that \( a \) does not succeed \( b \) but without explicitly stating its relation (whether \( a \) is less than or equal to \( b \)), we can represent this as:

\( a ⊁ b \)

Example 2:

In set theory, consider two sets \( A \) and \( B \) with their cardinalities expressed as \( |A| \) and \( |B| \) respectively. If the cardinality of set \( A \) does not succeed that of set \( B \), this relationship can be symbolized as:

\( |A| ⊁ |B| \)

The ⊁ symbol provides a nuanced way of expressing relationships without specifying exact nature (like being less than or equal). As always, the context in which the symbol is used plays a significant role in discerning its exact meaning.

Mathematical symbol 'Does Not Succeed'

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Codes for the ⊁ Symbol

The Symbol
Alt CodeAlt 8833
HTML Code⊁
HTML Entity⊁
CSS Code\2281
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 8833. 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: &#8833;</b>My symbol: ⊁

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

HTML TextOutput
<b>My symbol: &nsc;</b>My symbol: ⊁

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

CSS and HTML TextOutput
span:after {
content: "\2281";}
<span>My symbol:</span>
My symbol: ⊁

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

HTML TextOutput
<b>My symbol: &#x2281;</b>My symbol: ⊁
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2281 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+2281. 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 2281 turns into ⊁. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u2281. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u2281"
document.write("My symbol: " + str)
My symbol: ⊁