Neither Less-Than nor Greater-Than

The Mathematical Symbol "Neither Less-Than nor Greater-Than (≸)"

Unveiling the "Neither Less-Than nor Greater-Than" Symbol (≸)

The world of mathematics is replete with symbols that articulate intricate relationships and comparisons. One such symbol, often seen in advanced mathematical studies, is the ≸ symbol. Known as "Neither Less-Than nor Greater-Than", it effectively represents the concept of non-comparability or equivalence in certain contexts. Let's dive deeper into its usage and significance.

Understanding ≸

The ≸ symbol is an assertion of non-comparability. In contexts where standard ordering is applicable, it can simply mean equality. However, in settings where traditional ordering isn't meaningful, ≸ denotes that two entities cannot be ranked in a usual "less-than" or "greater-than" manner.

Example 1: Numbers

For real numbers, a and b, if \( a ≸ b \), it directly implies \( a = b \) since real numbers have a well-defined order.

Example 2: Complex Numbers

Consider complex numbers, where traditional ordering isn't defined. For complex numbers z1 and z2, stating \( z1 ≸ z2 \) signifies that neither is greater than or less than the other, emphasizing the non-comparability in the complex plane.

Realms of ≸ Application

The ≸ symbol is leveraged across diverse mathematical territories:

• Order Theory: In discussions about partially ordered sets where not all elements can be compared.
• Complex Analysis: Highlighting the non-orderability of complex numbers.
• Abstract Algebra: In certain algebraic structures where traditional ordering doesn't apply.

Its use is pivotal in contexts where conventional comparisons are not meaningful or where equality is the intended assertion.

In summary, the ≸ symbol, encapsulating "Neither Less-Than nor Greater-Than", holds significance in mathematical discourse, especially where conventional comparisons fall short. It stands as a testament to the vast and nuanced vocabulary of mathematical notation.

Are You Good at Mathematical Symbols?

Do you know, or can you guess, the technical symbols? Well, let's see! Show Instructions

Codes for the ≸ Symbol

The Symbol	≸	copy
Alt Code	Alt 8824	copy
HTML Code	≸	copy
HTML Entity	≸	copy
CSS Code	\2278	copy
Hex Code	≸	copy
Unicode	U+2278	copy

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 8824. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

(Method 3) Use the HTML Decimal Code (for webpages).

HTML Text	Output
<b>My symbol: &#8824;</b>	My symbol: ≸

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

HTML Text	Output
<b>My symbol: &ntlg;</b>	My symbol: ≸

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

CSS and HTML Text	Output
<style> span:after { content: "\2278";} </style> <span>My symbol:</span>	My symbol: ≸

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

HTML Text	Output
<b>My symbol: &#x2278;</b>	My symbol: ≸

On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2278 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+2278. 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:

Type	Output
2278 [Hold down Alt] [Press x]	≸ (The 2278 turns into ≸. Note that you can omit any leading zeros.)

In JavaScript, the syntax is \uXXXX. So, our example would be \u2278. (Note that the format is 4 hexadecimal characters.)

JavaScript Text	Output
let str = "\u2278" document.write("My symbol: " + str)	My symbol: ≸

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