Less-Than But Not Equal To

The Mathematical Symbol "Less-Than But Not Equal To (≨)"

Decoding the "Less-Than But Not Equal To" Symbol (≨): A Subtle Mathematical Relation

While the world of mathematics is awash with symbols, some notations stand out for their precision in capturing complex relationships. The ≨ or "Less-Than But Not Equal To" is a prime example. By extending the simple less-than relation, this symbol underscores a distinction while maintaining order. This lesson covers its implications further.

Diving Deep into the ≨ Symbol

The ≨ symbol captures two aspects: the classic ordinal relationship (less-than) and the inequality (not equal to). In essence, for two entities \( a \) and \( b \), the expression \( a ≨ b \) signifies that \( a \) is less than \( b \), but \( a \) is not equal to \( b \).

Example 1: Real Numbers

Considering two real numbers, let's say 3 and 5, the relationship is obvious:

3 < 5

However, when denoted with ≨, it re-emphasizes the inequality:

3 ≨ 5

This might seem redundant for simple numeric comparisons, but the distinction becomes crucial in contexts where inequality needs to be stressed.

Example 2: Algebraic Expressions

For two algebraic expressions, \( x + 2 \) and \( x + 5 \), when \( x = 1 \), both expressions evaluate to different results, 3 and 6 respectively. Thus:

\( x + 2 ≨ x + 5 \) when \( x = 1 \).

The ≨ symbol finds significant utility in advanced mathematics, especially in areas requiring rigorous proofs. It clarifies assumptions, making it explicit that not only is one entity smaller than the other, but they are unequivocally distinct.

In summary, the ≨ symbol is a fine illustration of how mathematical notations evolve to capture nuances. Its use aids in presenting arguments with clarity, ensuring that the nature of relationships between entities is conveyed unambiguously.

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 8808	copy
HTML Code	≨	copy
HTML Entity	≨	copy
CSS Code	\2268	copy
Hex Code	≨	copy
Unicode	U+2268	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 8808. 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: &#8808;</b>	My symbol: ≨

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

HTML Text	Output
<b>My symbol: &lnE;</b>	My symbol: ≨

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

CSS and HTML Text	Output
<style> span:after { content: "\2268";} </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: &#x2268;</b>	My symbol: ≨

On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2268 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+2268. 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
2268 [Hold down Alt] [Press x]	≨ (The 2268 turns into ≨. Note that you can omit any leading zeros.)

In JavaScript, the syntax is \uXXXX. So, our example would be \u2268. (Note that the format is 4 hexadecimal characters.)

JavaScript Text	Output
let str = "\u2268" document.write("My symbol: " + str)	My symbol: ≨

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