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Less-Than or Greater-Than

The Mathematical Symbol "Less-Than or Greater-Than (≶)"

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The "Less-Than or Greater-Than" Symbol (≶): A Mathematical Dichotomy

Mathematics is rich with symbols that convey specific relationships and conditions. One such symbol that encapsulates an either-or relationship is the ≶ symbol, signifying "Less-Than or Greater-Than." Let's delve deeper into the understanding and usage of this bifurcated symbol.

Understanding the ≶ Symbol

At its core, the ≶ symbol communicates a non-equal relationship between two quantities. When comparing two entities \( a \) and \( b \) with this symbol, \( a ≶ b \) tells us that \( a \) is either less than \( b \) or greater than \( b \), but not equal to \( b \).

Example 1: Number Comparison

Considering two numbers, 7 and 9:

7 ≶ 9 indicates that 7 is less than 9. It does not specify the exact relationship but excludes the possibility of equality.

Conversely, if we have 11 and 3:

11 ≶ 3 confirms that 11 is greater than 3.

Example 2: Algebraic Relations

For algebraic terms \( x \) and \( y \), if a given condition expresses:

\( x ≶ y \), it implies that \( x \) and \( y \) are not equal and that one is greater than the other.

Relevance and Application

The ≶ symbol finds its use in various mathematical and computational contexts:

  • Set Theory: Indicating elements that are distinct from a specific entity within a set.
  • Computational Logic: In computer programming, it can be used to ensure that two variables are not the same without specifying which is larger.
  • Mathematical Proofs: In proofs, where the distinctness of two entities needs to be emphasized without specifying the exact nature of their difference.

The true power of the ≶ symbol lies in its ability to concisely convey non-equivalence. While it might seem simple, this fundamental notion is critical in countless mathematical and computational scenarios where the equality condition must be explicitly excluded.

In summary, the ≶ symbol, representing "Less-Than or Greater-Than", serves as a testament to the expressiveness of mathematical notation. By simplifying complex conditions into a singular symbol, it streamlines discussions and analyses across various mathematical disciplines.

Mathematical symbol 'Less-Than or Greater-Than'

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Codes for the ≶ Symbol

The Symbol
Alt CodeAlt 8822
HTML Code≶
HTML Entity≶
CSS Code\2276
Hex Code≶
UnicodeU+2276

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 8822. 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: &#8822;</b>My symbol: ≶

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

HTML TextOutput
<b>My symbol: &lg;</b>My symbol: ≶

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

CSS and HTML TextOutput
<style>
span:after {
content: "\2276";}
</style>
<span>My symbol:</span>
My symbol: ≶

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

HTML TextOutput
<b>My symbol: &#x2276;</b>My symbol: ≶
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2276 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+2276. 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
2276
[Hold down Alt]
[Press x]

(The 2276 turns into ≶. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u2276. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u2276"
document.write("My symbol: " + str)
My symbol: ≶

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More about Mathematical Symbols

Mathematics is a universal language that is used to describe and understand the intricacies of the universe. At the heart of this language are symbols, concise representations that convey specific meanings and ideas.

Just as letters come together to form words in spoken languages, mathematical symbols combine to form expressions and equations, encapsulating intricate ideas in a compact form. The history of these symbols is as varied as their meanings; some have been in use for centuries while others have been introduced more recently to describe new discoveries and concepts. Whether you are a student, educator, researcher, or simply curious, this list of mathematical symbols will serve as a guide, shedding light on their meanings, origins, and applications.

From the simple plus and minus signs to the more esoteric and complex, each symbol has its unique story and significance.

More Symbols

Full List of Mathematical Symbols