Less-Than Sign

The Mathematical Symbol "Less-Than Sign (<)"

The "Less-Than Sign" (<): A Fundamental Relation in Mathematics

Among the myriad of symbols in mathematics, a few stand out for their foundational significance. The < or "Less-Than Sign" is one such notation. Universally recognized and ubiquitously used, this symbol establishes a basic ordinal relationship between numbers. This lesson covers its varied implications and applications.

Grasping the < Symbol

The < symbol, at its core, defines a basic order relation between numbers. If \( a \) and \( b \) are two numbers, then \( a < b \) signifies that \( a \) is less than \( b \). While most commonly used with real numbers, the concept of "less than" is foundational to many areas of mathematics.

Example 1: Real Numbers

For two real numbers, say 3 and 5, the relationship can be written as:

3 < 5

This indicates that 3 is less than 5.

Example 2: Algebraic Expressions

Consider two algebraic expressions \( x^2 \) and \( x^3 \) where \( x > 1 \). In this context, one can infer:

\( x^2 < x^3 \) for all \( x > 1 \).

The < symbol isn't limited to numbers and algebraic expressions. In more advanced areas of mathematics, similar "order relations" can be defined for more abstract entities, like matrices, functions, and even sets. Moreover, in computer programming and algorithm design, the < symbol plays a crucial role in condition-checking and loop constructs.

In summary, the < symbol's straightforward representation of an order relation is a cornerstone in mathematics, science, and programming. Its enduring presence across disciplines is a testament to its fundamental importance.

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 60	copy
HTML Code	&#60;	copy
HTML Entity	&lt;	copy
CSS Code	\003C	copy
Hex Code	&#x3C;	copy
Unicode	U+003C	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 60. 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: &#60;</b>	My symbol: <

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

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

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

CSS and HTML Text	Output
<style> span:after { content: "\003C";} </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: &#x003C;</b>	My symbol: <

On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x003C 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+003C. 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
003C [Hold down Alt] [Press x]	< (The 003C turns into <. Note that you can omit any leading zeros.)

In JavaScript, the syntax is \uXXXX. So, our example would be \u003C. (Note that the format is 4 hexadecimal characters.)

JavaScript Text	Output
let str = "\u003C" document.write("My symbol: " + str)	My symbol: <

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