Concept

Continuum (set theory)

In the mathematical field of set theory, the continuum means the real numbers, or the corresponding (infinite) cardinal number, denoted by . Georg Cantor proved that the cardinality is larger than the smallest infinity, namely, . He also proved that is equal to , the cardinality of the power set of the natural numbers. The cardinality of the continuum is the size of the set of real numbers. The continuum hypothesis is sometimes stated by saying that no cardinality lies between that of the continuum and that of the natural numbers, , or alternatively, that . Linear continuum According to Raymond Wilder (1965), there are four axioms that make a set C and the relation < into a linear continuum: C is simply ordered with respect to

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https://en.wikipedia.org/wiki/Continuum_(set_theory)

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Transfinite number

In mathematics, transfinite numbers or infinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers. These include the transfinite cardinals, which are cardinal numbers used to quantify the size of infinite sets, and the transfinite ordinals, which are ordinal numbers used to provide an ordering of infinite sets. The term transfinite was coined in 1895 by Georg Cantor, who wished to avoid some of the implications of the word infinite in connection with these objects, which were, nevertheless, not finite.

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