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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 } .
Transfinite numbers: Numbers that are greater than any natural number. Ordinal numbers: Finite and infinite numbers used to describe the order type of well-ordered sets. Cardinal numbers: Finite and infinite numbers used to describe the cardinalities of sets.
In a positional numeral system, the radix (pl.: radices) or base is the number of unique digits, including the digit zero, used to represent numbers.For example, for the decimal system (the most common system in use today) the radix is ten, because it uses the ten digits from 0 through 9.
Definition: a cardinal n is a natural number if and only if there exists a finite set of which the cardinal is n. 0 = Card (∅) 1 = Card({A}) = Card({∅}) Definition: the successor of a cardinal K is the cardinal K + 1 Theorem: the natural numbers satisfy Peano’s axioms
This article is about "positive integers" and "non-negative integers". For all the numbers ..., −2, −1, 0, 1, 2, ..., see Integer.
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A000040: Partition numbers P n:
A natural number is a sociable narcissistic number if it is a periodic point for , where () = for a positive integer (here is the th iterate of ), and forms a cycle of period . A narcissistic number is a sociable narcissistic number with p = 1 {\displaystyle p=1} , and an amicable narcissistic number is a sociable narcissistic number with p = 2 ...
The paradox states that every natural number is interesting. [1] The " proof " is by contradiction : if there exists a non-empty set of uninteresting natural numbers, there would be a smallest uninteresting number – but the smallest uninteresting number is itself interesting because it is the smallest uninteresting number, thus producing a ...