View source for Less-than sign

{{Short description|Mathematical symbol for "less than"}}
{{for|the use of the "&lt;" sign as punctuation | Bracket#Angle brackets}}
{{More references|date=June 2019}}
{{Infobox symbol
|mark=<
|name=Less-than sign
|unicode = {{unichar|003C|Less-than sign|html=}}
|see also= {{unichar|003E|GREATER-THAN SIGN|nlink=Greater-than sign}}<br/>{{unichar|2264|Less-than or equal to}}<br />
{{Unichar|2A7D|LESS-THAN OR SLANTED EQUAL TO}} used e.g. in Poland<br />
{{unichar|226E|NOT LESS-THAN}}<br />{{unichar|226A|Much less-than}} 
|different from = {{unichar|2329|Left-POINTING ANGLE BRACKET|nlink=Bracket#Angle brackets}}
}}
The '''less-than sign''' is a mathematical symbol that denotes an [[Inequality (mathematics)|inequality]] between two values. The widely adopted form of two equal-length strokes connecting in an [[acute angle]] at the left, {{char|<}}, 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 {{math|{{frac|1|2}} < 1}} and {{math|−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''', {{char|<}}, is an original [[ASCII]] character (hex 3C, decimal 60).

===Programming===
In [[BASIC]], [[Lisp (programming language)|Lisp]]-family languages, and [[C (programming language)|C]]-family languages (including [[Java (programming language)|Java]] and [[C++]]), [[Operator (computing)|comparison operator]] <code>&lt;</code> means "less than".

In [[Coldfusion]], operator <code>.lt.</code> means "less than".

In [[Fortran]], operator <code>.LT.</code> means "less than"; later versions allow <code>&lt;</code>.

====Shell scripts====
In [[Bourne shell]] (and many other shells), operator <code>-lt</code> means "less than". Less-than sign is used to [[Redirection (computing)|redirect]] input from a file. Less-than plus ampersand ({{code|<&}}) is used to redirect from a [[file descriptor]].

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

In [[Bash (Unix shell)|Bash]], [[Perl]], and [[Ruby (programming language)|Ruby]], operator {{code|<<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 (programming language)|C]] and [[C++]], operator {{code|<<}} represents a [[Bitwise operation#Shifts in C, C++, C#, Python|binary left shift]].

In the [[C++ Standard Library]], operator {{code|<<}}, when applied on an output stream, acts as ''insertion operator'' and performs an output operation on the stream.

In [[Ruby (programming language)|Ruby]], operator {{code|<<}} acts as ''append operator'' when used between an array and the value to be appended.

In [[XPath]] the {{code|<<}} operator returns true if the left operand precedes the right operand in document order; otherwise it returns false.<ref>{{cite web |date=14 December 2010 |title=XML Path Language (XPath) 2.0 (Second Edition) |url=https://www.w3.org/TR/xpath20/#id-node-comparisons |archive-url=https://web.archive.org/web/20221007124416/https://www.w3.org/TR/xpath20/#id-node-comparisons |archive-date=7 October 2022 |access-date=29 October 2019 |website=www.w3.org |publisher=W3C}}</ref>

====Triple less-than sign====
In [[PHP]], operator {{code|<<<OUTPUT}} is used to denote the beginning of a [[here document|heredoc]] statement (where <code>OUTPUT</code> is an arbitrary named variable.)

In Bash, {{code|<<<word}} is used as a "here string", where {{code|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, {{code|1=<=}}, may be used for an approximation of the [[Inequality (mathematics)|less-than-or-equal-to sign]], {{char|≤}}. ASCII does not have a less-than-or-equal-to sign, but [[Unicode]] defines it at code point U+2264.

In [[BASIC]], [[Lisp (programming language)|Lisp]]-family languages, and [[C (programming language)|C]]-family languages (including [[Java (programming language)|Java]] and [[C++]]), operator {{code|1=<=}} means "less than or equal to". In [[Sinclair BASIC]] it is encoded as a single-byte code point token.

In [[Prolog]], {{code|1==<}} means "less than or equal to" (as distinct from the arrow {{code|1=<=}}).

In [[Fortran]], operators {{code|.LE.}} and {{code|1=<=}} both mean "less than or equal to".

In [[Bourne shell]] and [[Windows PowerShell]], the operator {{code|-le}} means "less than or equal to".

====Less-than sign with hyphen-minus====
In the [[R (programming language)|R programming language]], the less-than sign is used in conjunction with a [[hyphen-minus]] to create an arrow ({{code|<-}}), 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 [[Standard Generalized Markup Language|SGML]] and [[XML]]), the less-than sign is used at the beginning of tags. The less-than sign may be included with <code>&amp;lt;</code>. The less-than-or-equal-to sign, {{char|≤}}, may be included with <code>&amp;le;</code>.

==Unicode==
[[Unicode]] provides various Less Than Symbols:<ref>{{Cite web |title=Less than symbol |url=https://lessthansymbol.com/ |access-date=2023-06-06 |archive-date=2023-05-16 |archive-url=https://web.archive.org/web/20230516200208/https://lessthansymbol.com/ |url-status=live }}</ref>
{| class="wikitable sortable" 
! Symbol !!  Unicode name !!  Code Point
|-
| < || {{sc|Less-Than Sign }} || U+003C
|-
| ≤ || {{sc|Less-Than Or Equal To }} || U+2264
|-
| ≦ || {{sc|Less-Than Over Equal To}} || U+2266
|-
| ≨ || {{sc|Less-Than But Not Equal To}} || U+2268
|-
| ≪ || {{sc|Much Less-Than}} || U+226A
|-
| ≮|| {{sc|Not Less Than}} || U+226E
|-
| ≰|| {{sc|Neither Less-Than Nor Equal To }} || U+2270
|-
| ≲ || {{sc|Less-Than Or Equivalent To }} || U+2272
|-
| ≴ || {{sc|Neither Less-Than Nor Equivalent To }} || U+2274
|-
| ⋖ || {{sc|Less-Than With Dot }} || U+22D6
|-
| ⋘ || {{sc|Very Much Less-Than }} || U+22D8
|-
| ⋜ || {{sc|Equal To Or Less-Than }} || U+22DC
|-
| ⋦ || {{sc|Less-Than But Not Equivalent To }} || U+22E6
|-
| ⍃ || {{sc|Apl Functional Symbol Quad Less-Than}} || U+2343
|-
| ⥶ || {{sc|Less-Than Above Leftwards Arrow }} || U+2976
|-
| ⥷ || {{sc|Leftwards Arrow Through Less-Than}} || U+2977
|-
| ⦓ || {{sc|Left Arc Less-Than Bracket }} || U+2993
|-
| ⦖ || {{sc|Double Right Arc Less-Than Bracket}} || U+2996
|-
| ⧀ || {{sc|Circled Less-Than}} || U+29C0
|-
| ⩹ || {{sc|Less-Than With Circle Inside }} || U+2A79
|-
| ⩻ || {{sc|Less-Than With Question Mark Above }} || U+2A7B
|-
| ⩽ || {{sc|Less-Than Or Slanted Equal To }} || U+2A7D
|-
| ⩿ || {{sc|Less-Than Or Slanted Equal To With Dot Inside }} || U+2A7F
|-
| ⪁ || {{sc|Less-Than Or Slanted Equal To With Dot Above }} || U+2A81
|-
| ⪃ || {{sc|Less-Than Or Slanted Equal To With Dot Above Right }} || U+2A83
|-
| ⪅ || {{sc|Less-Than Or Approximate }} || U+2A85
|-
| ⪇ || {{sc|Less-Than And Single-Line Not Equal To }} || U+2A87
|-
| ⪉ || {{sc|Less-Than And Not Approximate }} || U+2A89
|-
| ⪍ || {{sc|Less-Than Above Similar Or Equal }} || U+2A8D
|-
| ⪕ || {{sc|Slanted Equal Or Less-Than }} || U+2A95
|-
| ⪗ || {{sc|Slanted Equal Or Less-Than With Dot Inside }} || U+2A97
|-
| ⪙ || {{sc|Double-Line Equal To Or Less-Than }} || U+2A99
|-
| ⪛ || {{sc|Double-Line Slanted Equal To Or Less-Than }} || U+2A9B
|-
| ⪝ || {{sc|Similar To Or Less-Than }} || U+2A9D
|-
| ⪟ || {{sc|Similar Above Less-Than Above Equals Sign }} || U+2A9F
|-
| ⪡ || {{sc|Double Nested Less-Than }} || U+2AA1
|-
| ⪣ || {{sc|Double Nested Less-Than With Underbar}} || U+2AA3
|-
| ⪦ || {{sc|Less-Than Closed By Curve }} || U+2AA6
|-
| ⪨ || {{sc|Less-Than Closed By Curve Above Slanted Equal }} || U+2AA8
|-
| ⫷ || {{sc|Triple Nested Less-Than }} || U+2AF7
|-
| ⫹ || {{sc|Double-line Slanted Less-than Or Equal To }} || U+2AF9
|-
| ﹤ || {{sc|Small Less-Than Sign }} || U+FE64
|-
| ＜ || {{sc|Fullwidth Less-Than }} || U+FF1C
|}

The less-than sign may be seen for an approximation of the opening [[Bracket#Angle brackets|angle bracket]], {{char|⟨}}. True angle bracket characters, as required in [[Notation#Linguistics|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 {{char|<math>\prec </math>}} is often used when it would be confusing or not convenient to use {{char|<}}. In mathematical writing using [[LaTeX]], the [[TeX]] command is {{code|\prec }}. The Unicode [[code point]] is {{nobr|{{unichar|227A}}}}.

==See also==
*[[Inequality (mathematics)]]
*[[Greater-than sign]]
*[[Relational operator]]
*[[Much-less-than sign]]

==References==
{{Reflist}}

[[Category:Typographical symbols]]
[[Category:Mathematical symbols]]
[[Category:Inequalities]]