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Set - Special sets | | Set - Special sets: Encyclopedia II - Set - Special sets | | There are some sets which hold great mathematical importance and are referred to with such regularity that they have acquired special names to identify them. One of these is the empty set. Some special sets of numbers include:
denotes the set of all natural numbers. That is to say, = {1, 2, 3, ...}, or sometimes = {0, 1, 2, 3, ...}.
denotes the set of all integers (whether positive, negative or zero). So = {..., -2, -1, 0, 1, 2, ...}.
denotes the set of all rational numbers (that is, the set of all proper ...
See also:Set, Set - Definition, Set - Describing sets, Set - Descriptions using words or lists, Set - Descriptions using mathematical notation, Set - Set membership, Set - Cardinality of a set, Set - Subsets, Set - Special sets, Set - Unions, Set - Intersections, Set - Complements | | | Set, Set - Cardinality of a set, Set - Complements, Set - Definition, Set - Describing sets, Set - Descriptions using mathematical notation, Set - Descriptions using words or lists, Set - Intersections, Set - Set membership, Set - Special sets, Set - Subsets, Set - Unions, Alternative set theory, Class (set theory), Family (mathematics), Mathematical structure, Multiset, Tuple | | |
| | | Set: Encyclopedia II - Set - Special sets
Set - Special sets
There are some sets which hold great mathematical importance and are referred to with such regularity that they have acquired special names to identify them. One of these is the empty set. Some special sets of numbers include:
- denotes the set of all natural numbers. That is to say, = {1, 2, 3, ...}, or sometimes = {0, 1, 2, 3, ...}.
- denotes the set of all integers (whether positive, negative or zero). So = {..., -2, -1, 0, 1, 2, ...}.
- denotes the set of all rational numbers (that is, the set of all proper and improper fractions). So, = { : a,b and b ≠ 0}. For example, and . All integers are in this set since every integer a can be expressed as the fraction .
- is the set of all real numbers. This set includes all rational numbers, together with all irrational numbers (that is, numbers which can't be rewritten as fractions, such as π,
e, and √2).
- is the set of all complex numbers.
Each of these sets of numbers has infinite cardinality, and moreover .
Other related archives19th century, Alternative set theory, Class (set theory), Complement (set theory), Empty set, Family (mathematics), French flag, Intersection (set theory), Mathematical structure, Multiset, Set theory, Set-builder notation, Subset, Tuple, Union (set theory), axiomatic, axiomatic set theory, braces, cardinal number, cardinality, collection, combinatorics, complex numbers, concepts, elements, ellipsis, equality, expression, improper fractions, infinity, integers, intuitive, irrational, mathematics, mathematics education, multiset, naive set theory, natural numbers, permutations and combinations, powers of two, primary school, proper, rational numbers, real numbers, relationship, set theory, theory, universal set, whole, whole numbers
 Adapted from the Wikipedia article "Special sets", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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