Natural Numbers

Some articles on numbers, natural number, natural numbers, number:

Parity Of Zero - Mathematical Contexts - Even-odd Alternation
... even, together with the fact that even and odd numbers alternate, is enough to determine the parity of every other natural number ... This idea can be formalized into a recursive definition of the set of even natural numbers 0 is even ... of relying only on the minimal foundations of the natural numbers the existence of 0 and of successors ...
PRO (category Theory)
... monoidal category whose objects are the natural numbers (incl ... and whose tensor product is given on objects by the addition on numbers ... Some examples of PROs the discrete category of natural numbers, the category FinSet of natural numbers and functions between them, the category Bij of natural numbers and bijections ...
Fields of Mathematics - Pure Mathematics - Quantity
... The study of quantity starts with numbers, first the familiar natural numbers and integers ("whole numbers") and arithmetical operations on them, which are characterized in arithmetic ... The deeper properties of integers are studied in number theory, from which come such popular results as Fermat's Last Theorem ... and Goldbach's conjecture are two unsolved problems in number theory ...
Myhill's Constructive Set Theory
... Myhill's system CST is a constructive first-order logic with three sorts natural numbers, functions, and sets ... The usual Peano axioms for natural numbers ... of the axiom of infinity asserting that the collection of natural numbers (for which he introduces a constant N) is in fact a set ...
Container (type Theory)
... For lists, the shape type is the natural numbers (including zero) ... The corresponding position types are the types of natural numbers less than the shape, for each shape ... Note that the natural numbers are isomorphic to lists of units ...

Famous quotes containing the words numbers and/or natural:

    And when all bodies meet
    In Lethe to be drowned,
    Then only numbers sweet
    With endless life are crowned.
    Robert Herrick (1591–1674)

    What journeyings on foot and on horseback through the wilderness, to preach the gospel to these minks and muskrats! who first, no doubt, listened with their red ears out of a natural hospitality and courtesy, and afterward from curiosity or even interest, till at length there “were praying Indians,” and, as the General Court wrote to Cromwell, the “work is brought to this perfection that some of the Indians themselves can pray and prophesy in a comfortable manner.”
    Henry David Thoreau (1817–1862)