“Continuum”的概念、定义、习题解题方法及翻译-数学辞典

单词

Continuum

释义

Continuum

The nondenumerable set of Real Numbers, denoted . It satisfies

(1)

and

(2)

where

is Aleph-0. It is also true that

(3)

However,

(4)

is a Set larger than the continuum. Paradoxically, there are exactly as many points

on a Line (orLine Segment) as in a Plane, a 3-D Space, or finite Hyperspace, since all these Sets can be put into a One-to-One correspondence with each other.

The Georg Cantor, holds that theCardinal Number of the continuum is the same as that of Aleph-1. The surprising truth isthat this proposition is Undecidable, since neither it nor its converse contradicts the tenets of SetTheory.

See also Aleph-0, Aleph-1, Continuum Hypothesis,Denumerable Set

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