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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 ...
The cardinality of the natural numbers is ℵ 0 (read aleph-nought, aleph-zero, or aleph-null), the next larger cardinality of a well-ordered set is aleph-one ℵ 1, then ℵ 2 and so on. Continuing in this manner, it is possible to define a cardinal number ℵ α for every ordinal number α , as described below.
Every finite or countably infinite subset of the real numbers is a null set. For example, the set of natural numbers , the set of rational numbers and the set of algebraic numbers are all countably infinite and therefore are null sets when considered as subsets of the real numbers.
Null symbol may refer to: Null character , U+0000 <control-0000> , U+2400 ␀ SYMBOL FOR NULL (a single-character glyph "NUL") Null sign (∅), the empty set
The empty set is the set containing no elements. 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.
It is often abbreviated as NUL (or NULL, though in some contexts that term is used for the null pointer). In 8-bit codes, it is known as a null byte . The original meaning of this character was like NOP —when sent to a printer or a terminal , it has no effect (some terminals, however, incorrectly display it as space ).
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In pronoun-dropping languages, including null subject languages such as most Romance languages, the zero pronoun is a prominent feature. A zero subordinate conjunction occurs in English in sentences like I know ∅ he likes me, in which the zero conjunction plays the role of the subordinate conjunction that in I know that he likes me.