Null sign

In mathematics, the null sign (∅) denotes the 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 Norwegian and Danish alphabets (and not related in any way to the Greek letter Φ).^[1]

In linguistics, the null sign is used to indicate the absence of an element, such as a sound or morpheme. For example, "I went to ∅ party" indicates that the usual determiner (perhaps "a" or "the") is missing.

It is also used in distinguishing the symbol null from zero (0).

Applications

Null sets are used in set operations.

For example:

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

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

A∩B=?

There are no common element/s on the solution so it should be denoted as:

A∩B=∅ or A∩B={ }

Phonetics

Null signs in phonetics is used in lost sounds or morphemes (they are not schwa sounds).

A word with a silent sound is denoted by the symbol ∅.Often used in lost morphemes.

Null Morphemes

First used 2000 years ago.It is an invisible affix used by a Sanskrit grammarian in India.

Existence

Commonly in singular form of nouns,next to the noun.

For example: Mango=Mango+ 0 or ∅ Banana=Banana+ 0 or ∅

To simplify,∅ is a contrast of -s,-es,-ies and -ves.

In some cases,the null sign is a sign also to indicate plurality.

For example:

Singular Form: Sheep=Sheep+ 0 or ∅ Plural Form: Sheep=Sheep+ 0 or ∅

They are singular and plural in form so they have both null morphemes.

References

1. Earliest Uses of Symbols of Set Theory and Logic.