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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| List of numbers | 1/2 | https://en.wikipedia.org/wiki/List_of_numbers | reference | science, encyclopedia | 2026-05-05T08:19:08.279774+00:00 | kb-cron |
This is a list of notable numbers and articles about them. The list does not contain all numbers in existence as most of the number sets are infinite. Numbers may be included in the list based on their mathematical, historical or cultural notability, but all numbers have qualities that could arguably make them notable. Even the smallest "uninteresting" number is paradoxically interesting for that very property. This is known as the interesting number paradox. The definition of what is classed as a number is rather diffuse and based on historical distinctions. For example, the pair of numbers (3,4) is commonly regarded as a number when it is in the form of a complex number (3+4i), but not when it is in the form of a vector (3,4). This list will also be categorized with the standard convention of types of numbers. This list focuses on numbers as mathematical objects and is not a list of numerals, which are linguistic devices: nouns, adjectives, or adverbs that designate numbers. The distinction is drawn between the number five (an abstract object equal to 2+3), and the numeral five (the noun referring to the number).
== Natural numbers ==
Natural numbers are a subset of the integers and are of historical and pedagogical value as they can be used for counting and often have ethno-cultural significance (see below). Beyond this, natural numbers are widely used as a building block for other number systems including the integers, rational numbers and real numbers. Natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country"). In common language, words used for counting are "cardinal numbers" and words used for ordering are "ordinal numbers". Defined by the Peano axioms, the natural numbers form an infinitely large set. Often referred to as "the naturals", the natural numbers are usually symbolised by a boldface N (or blackboard bold
N
{\displaystyle \mathbb {\mathbb {N} } }
, Unicode U+2115 ℕ DOUBLE-STRUCK CAPITAL N). The inclusion of 0 in the set of natural numbers is ambiguous and subject to individual definitions. In set theory and computer science, 0 is typically considered a natural number. In number theory, it usually is not. The ambiguity can be solved with the terms "non-negative integers", which includes 0, and "positive integers", which does not. Natural numbers may be used as cardinal numbers, which may go by various names. Natural numbers may also be used as ordinal numbers.
=== Mathematical significance === Natural numbers may have properties specific to the individual number or may be part of a set (such as prime numbers) of numbers with a particular property.
=== Cultural or practical significance === Along with their mathematical properties, many integers have cultural significance or are also notable for their use in computing and measurement. As mathematical properties (such as divisibility) can confer practical utility, there may be interplay and connections between the cultural or practical significance of an integer and its mathematical properties.
== Classes of natural numbers == Subsets of the natural numbers, such as the prime numbers, may be grouped into sets, for instance based on the divisibility of their members. Infinitely many such sets are possible. A list of notable classes of natural numbers may be found at classes of natural numbers.
=== Prime numbers ===
A prime number is a positive integer which has exactly two divisors: 1 and itself. The first 100 prime numbers are:
=== Highly composite numbers ===
A highly composite number (HCN) is a positive integer with more divisors than any smaller positive integer. They are often used in geometry, grouping and time measurement. The first 20 highly composite numbers are: 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560
=== Perfect numbers ===
A perfect number is an integer that is the sum of its positive proper divisors (all divisors except itself). The first 10 perfect numbers:
== Integers ==
The integers are a set of numbers commonly encountered in arithmetic and number theory. There are many subsets of the integers, including the natural numbers, prime numbers, perfect numbers, etc. Many integers are notable for their mathematical properties. Integers are usually symbolised by a boldface Z (or blackboard bold
Z
{\displaystyle \mathbb {\mathbb {Z} } }
, Unicode U+2124 ℤ DOUBLE-STRUCK CAPITAL Z); this became the symbol for the integers based on the German word for "numbers" (Zahlen). Notable integers include −1, the additive inverse of unity, and 0, the additive identity. As with the natural numbers, the integers may also have cultural or practical significance. For instance, −40 is the equal point in the Fahrenheit and Celsius scales.
=== SI prefixes === One important use of integers is in orders of magnitude. A power of 10 is a number 10k, where k is an integer. For instance, with k = 0, 1, 2, 3, ..., the appropriate powers of ten are 1, 10, 100, 1000, ... Powers of ten can also be fractional: for instance, k = -3 gives 1/1000, or 0.001. This is used in scientific notation, real numbers are written in the form m × 10n. The number 394,000 is written in this form as 3.94 × 105. Integers are used as prefixes in the SI system. A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit. Each prefix has a unique symbol that is prepended to the unit symbol. The prefix kilo-, for example, may be added to gram to indicate multiplication by one thousand: one kilogram is equal to one thousand grams. The prefix milli-, likewise, may be added to metre to indicate division by one thousand; one millimetre is equal to one thousandth of a metre.
== Rational numbers ==