Search results
Results From The WOW.Com Content Network
In mathematics, the empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. [1] Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set , while in other theories, its existence can be deduced.
Note that a null set is not necessarily an empty set. Common notations for the empty set include "{}", "∅", and "". 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). [2] Empty sets ...
Deutsch: Dieses Dokument listet 20323 Symbole und die dazugehörigen LaTeX-Befehle auf. Manche Symbole sind in jedem LaTeX-2ε-System verfügbar; andere benötigen zusätzliche Schriftarten oder Pakete, die nicht notwendig in jeder Distribution mitgeliefert werden und daher selbst installiert werden müssen.
In set theory, the empty set, that is, the set with zero elements, denoted "{}" or "∅", may also be called null set. [3] [5] In measure theory, a null set is a (possibly nonempty) set with zero measure. A null space of a mapping is the part of the domain that is mapped into the null element of the image (the inverse image of the null element).
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
Note that the above should not be confused with the "slashed zero variant of the empty set", , as popularized by Donald Knuth's TeX. [8] Unicode represents that character as the empty set (∅) with variation selector 1. [7] Prior to Unicode 9.0, there was no code point defined for altering the visual appearance of zero.
It is a useful concept in analysis, indicating lack of an element where one might be expected. It is usually written with the symbol "∅", in Unicode U+2205 ∅ EMPTY SET (∅, ∅, ∅, ∅). A common ad hoc solution is to use the Scandinavian capital letter Ø instead. There are several kinds of zero:
The glyph of the up tack appears as an upside-down tee symbol, and as such is sometimes called eet (the word "tee" in reverse). [citation needed] Tee plays a complementary or dual role in many of these theories. The similar-looking perpendicular symbol ( , \perp in LaTeX, U+27C2 in Unicode) is a binary relation symbol used to represent: