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.
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 <. The less-than-or-equal-to sign, ≤, may be included with ≤.
Unicode
Unicode provides various less than symbols:2
| Symbol | Unicode name | Code Point |
|---|---|---|
| < | 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 ≺ {\displaystyle \prec } 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 ≺ PRECEDES.
See also
References
"XML Path Language (XPath) 2.0 (Second Edition)". www.w3.org. W3C. 14 December 2010. Archived from the original on 7 October 2022. Retrieved 29 October 2019. https://web.archive.org/web/20221007124416/https://www.w3.org/TR/xpath20/#id-node-comparisons ↩
"Less than symbol". Archived from the original on 2023-05-16. Retrieved 2023-06-06. https://lessthansymbol.com/ ↩