Null sign

{{Short description|Sign representing zero or empty set}}

{{hatnote|This article is about mathematical notation. For a null unit of semiotic meaning, see Empty string or Zero (linguistics)}}

{{Other uses|Null symbol (disambiguation)|Ø (disambiguation)}}

File:Atheism symbol syreeni.svg

The null sign (∅) is a symbol often used in mathematics for denoting the empty set. The same letter in linguistics represents zero, the lack of an element. It is commonly used in phonology, morphology, and syntax.

Encodings

The symbol ∅ is available at Unicode point U+2205.[https://www.unicode.org/charts/PDF/U2200.pdf Unicode Standard 5.2] It can be coded in HTML as {{mono|∅}} and as {{mono|∅}} or as {{mono|∅}}. It can be coded in LaTeX as {{mono|\varnothing}}.

Similar letters

Similar letters and symbols include the following:

Use in mathematics

In mathematics, the null sign (∅) denotes the empty set.{{cite web |last1=Lankham |first1=Isaiah |last2=Nachtergaele |first2=Bruno |last3=Schilling |first3=Anne |title=Some Common Mathematical Symbols and Abbreviations (with History) |url=https://www.math.ucdavis.edu/~anne/WQ2007/mat67-Common_Math_Symbols.pdf |website=University of California, Davis |access-date=2 May 2025 |page=2 |date=January 21, 2007}}{{cite book |last1=Gerstein |first1=Larry J. |title=Introduction to Mathematical Structures and Proofs |date=2012 |publisher=Springer |location=New York |isbn=9781461442653 |pages=42-43 |url=https://www.google.com.au/books/edition/Introduction_to_Mathematical_Structures/qK9y768b1NQC?hl=en&gbpv=0 |access-date=2 May 2025}} Note that a null set is not necessarily an empty set. Common notations for the empty set include "{}", "∅", and "\emptyset". The latter two symbols were introduced by the Bourbaki group (specifically André Weil) in 1939, inspired by the letter Ø in the Danish and Norwegian alphabets (and not related in any way to the Greek letter Φ).{{cite web|url=http://jeff560.tripod.com/set.html|title=Earliest Uses of Symbols of Set Theory and Logic|website=jeff560.tripod.com}}

Empty sets are used in set operations. For example:

A=\{2,3,5,7,11\}

B=\{4,6,8,9\}

A \cap B = ?

There are no common elements in the solution; so it should be denoted as:

A \cap B = \varnothing or A \cap B = \{ \}

Use in linguistics

{{See also|Zero (linguistics)|Silent letter|Null morpheme}}

In linguistics, the null sign is used to indicate the absence of an element, such as a phoneme or morpheme.{{cite book |last1=Pullum |first1=Geoffrey K. |last2=Ladusaw |first2=William A. |title=Phonetic Symbol Guide |date=2013 |publisher=University of Chicago Press |isbn=9780226924885 |pages=136-137 |url=https://www.google.com.au/books/edition/Phonetic_Symbol_Guide/b7ml0qh2HMcC?hl=en&gbpv=1 |access-date=2 May 2025}}

=Morphology=

The English language was a fusional language, this means the language makes use of inflectional changes to convey multiple grammatical meanings. Although the inflectional complexity of English has been largely reduced in the course of development, the inflectional endings can be seen in earlier forms of English, such as Early Modern English (abbreviated as EModE).

The verb endings of EModE were summarised in the table below by Roger Lass:Lass, R. (1999). Phonology and Morphology. In R. Lass (Ed.), The Cambridge History of the English Language: 1476-1776 (Vol. 3, pp. 137-180). Cambridge, UK: Cambridge University Press.

class="wikitable" style="text-align: center;

|+ Verb Endings of EModE

PresentPast
First person singular-∅-d
Second person singular-st-dst
Third person singular-th, -s-d

Use in photography

In photography the null sign, Ø, found on camera lenses denotes the filter thread diameter, measured in millimeters. This marking indicates the size of screw-in filters that can be attached to the front of the lens. This diameter is separate from any optical specification of the lens, as it is a standardized measurement for photographers to select a compatible filter. Common filter thread sizes include 52mm, 72mm, 77mm, and 82mm. If a photographer owns multiple lenses with different filter thread diameters, stepping rings can be utilized to adapt larger filters to smaller lens threads, eliminating the need to purchase duplicate filters in various sizes.

References