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Denumerable infinity is orderly, whereas nondenumerable infinity is not at all so, being beyond order and disorder, and that "beyond" can be thought only as a sort of chaos.
Let R be the poset product of a k-element chain by a denumerable antichain.
The point-set that the early intuitionists accepted as constructible was even smaller than the continuum outlined by the grammarian orientation; its power did not exceed the denumerable and so it could not be identified, even provisionally, with the power set of the natural numbers.
A social system's characteristics that are denumerable become the observers' sources of information.
There is a base level and then a denumerable number of successive levels.
The German mathematician Georg Ferdinand Ludwig Philipp Cantor (1845-1918) used this sort of one-to-one correspondence to show that all fractions are denumerable and can be counted by the integers.
Georgescu-Roegen (1979) wanted a "systematic description of actuality with the aid of arithmomorphic concepts" and emphasized that "infinite space can accommodate at most a denumerable infinity of three-dimensional objects (as the traders must necessarily be).
The number of elements in one of these denumerable sets is called the cardinal number, or cardinality.
Endowed with the topology [tau] of uniform convergence on denumerable compact subsets of [0,1], it is a complete locally m-convex algebra.
Denumerable Markov chains; generating functions, boundary theory, random walks on trees.
Note that, the former of these requires a denumerable version of (AC) (= Axiom of Choice); and the latter one is based on the Zorn Maximality Principle (equivalent with (AC)).
In the thin set universe, these denumerable subsets are not included, only those which can be directly counted are added on to the spine of ordinals.
For adding one more entity to a denumerable infinity of entities does not increase the cardinality of the number of entities.
In place of that Miller imagines this throw as the last in a hypothetical sequence consisting of a denumerable infinity of repetitions at ever shorter intervals during the finite time interval (-1, 0), and also as the first in a converse sequence during the finite time interval (0, 1):
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