uncountable set

(redirected from Nondenumerable)

uncountable set

[¦ən′kau̇nt·ə·bəl ′set]
(mathematics)
An infinite set which cannot be put in one-to-one correspondence with the set of integers; for example, the set of real numbers.
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I think it is important to note a key aspect of the Deleuzo-Guattarian schema (and this is where the Badiouian treatment of this question, in Saint Paul for example, is really out of focus since it reduces the production of connective singularities to mere identitarian particularities): of course you have the majority, a redundant majority, and you have minorities, but Deleuze and Guattari write explicitly that the minorities regress to subsets as soon as they lose their quality of nondenumerable and cancerous flow.
Later, in his now famous speech given to the International Conference of Mathematicians at Paris in 1900, David Hilbert posed as his first problem (of 23) whether there are any nondenumerable sets whose cardinal numbers lie between [N.sub.0] and c.
(5) The types of reductions that he analyses--not only from the continuous to the discrete, but from the problematic to the axiomatic, the intensive to the extensive, the nonmetric to the metric, the nondenumerable to the denumerable, the rhizomatic to the arborescent, the smooth to the striated, and so on--while interrelated, are not identical, and each would have to be analyzed on its own account.
card(A) = [N.sub.0] indicates that the cardinal of a denumerable set A is infinite as opposed to card(A) = [infinity], denoting the infinity cardinal of a nondenumerable set A,
Furthermore, all real numbers correspond to the points in a line, so that points are also nondenumerable.