Null Sign
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Null Sign
Empty set symbols

The null sign EMPTY SET denotes the empty set in mathematics. 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.[1] It can be coded in HTML as &empty; and as &#8709;. It can be coded in LaTeX as \varnothing.

## Similar letters

Similar letters and symbols include the following:

## Use in mathematics

In mathematics, the null sign (?) denotes the empty set. Note that a null set is not necessarily an empty set. Common notations for the empty set include "{}", "?", and "${\displaystyle \emptyset }$". 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 ?).[2]

Empty sets are used in set operations. For example:

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

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

${\displaystyle A\cap B=?}$

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

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

## Use in linguistics

In linguistics, the null sign is used to indicate the absence of an element, such as a phoneme or morpheme.

### Morphology

The English language was a fusional language, this means the language makes use of inflectional changes to convey 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 the Early Modern English (abbreviated as EModE).

The verb endings of EModE was summarised in the table below by Professor Roger Lass:[3]

Verb Endings of EModE
Present Past
First person singular -? -d
Second person singular -st -dst
Third person singular -th, -s -d

## References

1. ^ Unicode Standard 5.2
2. ^ "Earliest Uses of Symbols of Set Theory and Logic". jeff560.tripod.com.
3. ^ 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.