The Mathematical Symbol "Less-Than or Equivalent To (≲)"

Exploring the "Less-Than or Equivalent To" Symbol (≲): Bridging Order and Similarity

Mathematics, with its vast array of symbols, provides unique tools to articulate specific relationships with precision. Among these tools, the ≲ or "Less-Than or Equivalent To" symbol offers a blend of ordinal relation with a notion of similarity or approximation. This article aims to shed light on the utility and significance of this particular notation.

Interpreting the ≲ Symbol

The ≲ symbol is a versatile notation, primarily capturing two concepts: an item being less than another and a notion of equivalence or similarity. When \( a \) and \( b \) are given entities, stating \( a ≲ b \) suggests that either \( a \) is less than \( b \) or \( a \) is approximately equal to \( b \).

Example 1: Number Comparison

For two real numbers, say 3.9 and 4, one could argue:

3.9 ≲ 4

Here, 3.9 is less than 4, but due to their proximity, they might be considered equivalent in certain contexts.

Example 2: Function Approximation

Consider the scenario where \( f(x) \) is a complex function and \( g(x) \) is its simpler approximation. If the difference between their values is negligible for a certain range of \( x \), one might express:

\( f(x) ≲ g(x) \) for that range of \( x \).

It's noteworthy that the symbol's exact interpretation often hinges on the context. In some mathematical scenarios, ≲ may be specifically defined in terms of a tolerance level for the approximation.

In summary, the ≲ symbol embodies a sophisticated blend of order and approximation, allowing mathematicians to express nuanced relationships with elegance. Whether used to compare numbers, functions, or other mathematical entities, its ability to communicate both difference and similarity is invaluable.

Mathematical symbol 'Less-Than or Equivalent To'

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Codes for the ≲ Symbol

The Symbol
Alt CodeAlt 8818
HTML Code≲
HTML Entity≲
CSS Code\2272
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 8818. 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: &#8818;</b>My symbol: ≲

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

HTML TextOutput
<b>My symbol: &lsim;</b>My symbol: ≲

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

CSS and HTML TextOutput
span:after {
content: "\2272";}
<span>My symbol:</span>
My symbol: ≲

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

HTML TextOutput
<b>My symbol: &#x2272;</b>My symbol: ≲
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2272 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+2272. 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 2272 turns into ≲. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u2272. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u2272"
document.write("My symbol: " + str)
My symbol: ≲