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A natural number can be used to express the size of a finite set; more precisely, a cardinal number is a measure for the size of a set, which is even suitable for infinite sets. The numbering of cardinals usually begins at zero, to accommodate the empty set. ∅ {\displaystyle \emptyset }
The natural numbers, starting with 1. The most familiar numbers are the natural numbers (sometimes called whole numbers or counting numbers): 1, 2, 3, and so on. Traditionally, the sequence of natural numbers started with 1 (0 was not even considered a number for the Ancient Greeks.)
Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds. Algebraic integer: A root of a monic polynomial with integer coefficients. Non-standard numbers. Transfinite numbers: Numbers that are greater than any natural number.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
An integer is the number zero (), a positive natural number (1, 2, 3, . . .), or the negation of a positive natural number (−1, −2, −3, . . .). The negations or additive inverses of the positive natural numbers are referred to as negative integers.
In Zermelo–Fraenkel (ZF) set theory, the natural numbers are defined recursively by letting 0 = {} be the empty set and n + 1 (the successor function) = n ∪ {n} for each n. In this way n = {0, 1, …, n − 1} for each natural number n. This definition has the property that n is a set with n elements. The first few numbers defined this way ...
Axiomatic definitions. An axiomatic definition of the real numbers consists of defining them as the elements of a complete ordered field. This means the following: The real numbers form a set, commonly denoted , containing two distinguished elements denoted 0 and 1, and on which are defined two binary operations and one binary relation; the operations are called addition and multiplication of ...
By culture / time period "A base is a natural number B whose powers (B multiplied by itself some number of times) are specially designated within a numerical system.": 38 The term is not equivalent to radix, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers.
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