Less-than sign

Short description: Mathematical symbol for "less than"

For the use of the "<" sign as punctuation, see Bracket § Angle brackets.

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Less-than sign

In Unicode| U+003C < LESS-THAN SIGN (HTML `&#60;` · `&lt;`)
Related
See also| similar symbols listed below

The less-than sign is a mathematical symbol that denotes an inequality between two values. The widely adopted form of two equal-length strokes connecting in an acute angle at the left, <, has been found in documents dated as far back as the 1560s. In mathematical writing, the less-than sign is typically placed between two values being compared and signifies that the first number is less than the second number. Examples of typical usage include 1 < 4 and −2 < 0.

Since the development of computer programming languages, the less-than sign and the greater-than sign have been repurposed for a range of uses and operations.

## Contents

* 1 Computing
* 1.1 Programming
* 1.1.1 Shell scripts
* 1.1.2 Double less-than sign
* 1.1.3 Triple less-than sign
* 1.1.4 Less-than sign with equals sign
* 1.1.5 Less-than sign with hyphen-minus
* 1.1.6 Spaceship operator
* 1.1.7 HTML
* 2 Unicode
* 3 Mathematics
* 4 See also
* 5 References

## Computing

The less-than sign, <, is an original ASCII character (hex 3C, decimal 60).

### Programming

In BASIC, Lisp-family languages, and C-family languages (including Java and C++), comparison operator `<` means "less than".

In Coldfusion, operator `.lt.` means "less than".

In Fortran, operator `.LT.` means "less than"; later versions allow `<`.

#### Shell scripts

In Bourne shell (and many other shells), operator `-lt` means "less than". Less-than sign is used to redirect input from a file. Less-than plus ampersand (`<&`) is used to redirect from a file descriptor.

#### Double less-than sign

The double less-than sign, <<, may be used for an approximation of the much-less-than sign (≪) or of the opening guillemet («). ASCII does not encode either of these signs, though they are both included in Unicode.

In Bash, Perl, and Ruby, operator `<<EOF` (where "EOF" is an arbitrary string, but commonly "EOF" denoting "end of file") is used to denote the beginning of a here document.

In C and C++, operator `<<` represents a binary left shift.

In the C++ Standard Library, operator `<<`, when applied on an output stream, acts as insertion operator and performs an output operation on the stream.

In Ruby, operator `<<` acts as append operator when used between an array and the value to be appended.

In XPath the `<<` operator returns true if the left operand precedes the right operand in document order; otherwise it returns false.[1]

#### Triple less-than sign

In PHP, operator `<<<OUTPUT` is used to denote the beginning of a heredoc statement (where `OUTPUT` is an arbitrary named variable.)

In Bash, `<<<word` is used as a "here string", where `word` is expanded and supplied to the command on its standard input, similar to a heredoc.

#### Less-than sign with equals sign

The less-than sign with the equals sign, `<=`, may be used for an approximation of the less-than-or-equal-to sign, ≤. ASCII does not have a less-than-or-equal-to sign, but Unicode defines it at code point U+2264.

In BASIC, Lisp-family languages, and C-family languages (including Java and C++), operator `<=` means "less than or equal to". In Sinclair BASIC it is encoded as a single-byte code point token.

In Prolog, `=<` means "less than or equal to" (as distinct from the arrow `<=`).

In Fortran, operators `.LE.` and `<=` both mean "less than or equal to".

In Bourne shell and Windows PowerShell, the operator `-le` means "less than or equal to".

#### Less-than sign with hyphen-minus

In the R programming language, the less-than sign is used in conjunction with a hyphen-minus to create an arrow (`<-`), this can be used as the left assignment operator.

#### Spaceship operator

The less-than sign is used in the spaceship operator.

#### HTML

In HTML (and SGML and XML), the less-than sign is used at the beginning of tags. The less-than sign may be included with `&lt;`. The less-than-or-equal-to sign, ≤, may be included with `&le;`.

## Unicode

Unicode provides various less than symbols:[2]

Symbol | Unicode name | Code Point

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< | LESS-THAN SIGN | U+003C
≤ | LESS-THAN OR EQUAL TO | U+2264
≦ | LESS-THAN OVER EQUAL TO | U+2266
≨ | LESS-THAN BUT NOT EQUAL TO | U+2268
≪ | MUCH LESS-THAN | U+226A
≮ | NOT LESS THAN | U+226E
≰ | NEITHER LESS-THAN NOR EQUAL TO | U+2270
≲ | LESS-THAN OR EQUIVALENT TO | U+2272
≴ | NEITHER LESS-THAN NOR EQUIVALENT TO | U+2274
⋖ | LESS-THAN WITH DOT | U+22D6
⋘ | VERY MUCH LESS-THAN | U+22D8
⋜ | EQUAL TO OR LESS-THAN | U+22DC
⋦ | LESS-THAN BUT NOT EQUIVALENT TO | U+22E6
⍃ | APL FUNCTIONAL SYMBOL QUAD LESS-THAN | U+2343
⥶ | LESS-THAN ABOVE LEFTWARDS ARROW | U+2976
⥷ | LEFTWARDS ARROW THROUGH LESS-THAN | U+2977
⦓ | LEFT ARC LESS-THAN BRACKET | U+2993
⦖ | DOUBLE RIGHT ARC LESS-THAN BRACKET | U+2996
⧀ | CIRCLED LESS-THAN | U+29C0
⩹ | LESS-THAN WITH CIRCLE INSIDE | U+2A79
⩻ | LESS-THAN WITH QUESTION MARK ABOVE | U+2A7B
⩽ | LESS-THAN OR SLANTED EQUAL TO | U+2A7D
⩿ | LESS-THAN OR SLANTED EQUAL TO WITH DOT INSIDE | U+2A7F
⪁ | LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE | U+2A81
⪃ | LESS-THAN OR SLANTED EQUAL TO WITH DOT ABOVE RIGHT | U+2A83
⪅ | LESS-THAN OR APPROXIMATE | U+2A85
⪇ | LESS-THAN AND SINGLE-LINE NOT EQUAL TO | U+2A87
⪉ | LESS-THAN AND NOT APPROXIMATE | U+2A89
⪍ | LESS-THAN ABOVE SIMILAR OR EQUAL | U+2A8D
⪕ | SLANTED EQUAL OR LESS-THAN | U+2A95
⪗ | SLANTED EQUAL OR LESS-THAN WITH DOT INSIDE | U+2A97
⪙ | DOUBLE-LINE EQUAL TO OR LESS-THAN | U+2A99
⪛ | DOUBLE-LINE SLANTED EQUAL TO OR LESS-THAN | U+2A9B
⪝ | SIMILAR TO OR LESS-THAN | U+2A9D
⪟ | SIMILAR ABOVE LESS-THAN ABOVE EQUALS SIGN | U+2A9F
⪡ | DOUBLE NESTED LESS-THAN | U+2AA1
⪣ | DOUBLE NESTED LESS-THAN WITH UNDERBAR | U+2AA3
⪦ | LESS-THAN CLOSED BY CURVE | U+2AA6
⪨ | LESS-THAN CLOSED BY CURVE ABOVE SLANTED EQUAL | U+2AA8
⫷ | TRIPLE NESTED LESS-THAN | U+2AF7
⫹ | DOUBLE-LINE SLANTED LESS-THAN OR EQUAL TO | U+2AF9
﹤ | SMALL LESS-THAN SIGN | U+FE64
＜ | FULLWIDTH LESS-THAN | U+FF1C

The less-than sign may be seen for an approximation of the opening angle bracket, ⟨. True angle bracket characters, as required in linguistics notation, are expected in formal texts.

## Mathematics

In an inequality, the less-than sign and greater-than sign always "point" to the smaller number. Put another way, the "jaws" (the wider section of the symbol) always direct to the larger number.

The less-than-sign is sometimes used to represent a total order, partial order or preorder. However, the symbol ≺ is often used when it would be confusing or not convenient to use <. In mathematical writing using LaTeX, the TeX command is `\prec`. The Unicode code point is U+227A ≺ .

## See also

* Inequality (mathematics)
* Greater-than sign
* Relational operator
* Much-less-than sign

## References

1. ↑ "XML Path Language (XPath) 2.0 (Second Edition)". W3C. 14 December 2010. https://www.w3.org/TR/xpath20/#id-node-comparisons.
2. ↑ "Less than symbol". https://lessthansymbol.com/.

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