transfinite number
transfinite number
English
Noun
Ad
Definition
Any cardinal or ordinal number which is larger than any finite, i.e. natural number; often represented by the Hebrew letter aleph (ℵ) with a subscript 0, 1, etc.
Example Sentences
- "It will be recalled that Cantor called the first transfinite number ℵ₀. He called the second transfinite number—the one describing the set of all real numbers— C. It has not been proved whether C is the next transfinite number after ℵ₀ or whether another number exists between them."
- "Let R be a bicompact of dimensionality #92;operatorname#123;ind#125;(R)#92;le#92;alpha. If #92;alpha is an isolated transfinite number, than ^([sic]) at any point x#92;inR there exist arbitrarily small neighborhoods Vx with boundaries of dimensionality #92;operatorname#123;ind#125;#92;overline#123;Vx#125;#92;le#92;alpha-1."
- "After all, it was the ordinals that made precise definition of the transfinite cardinals possible. And until Cantor had introduced the order types of transfinite number classes, he could not define precisely any transfinite cardinal beyond the first power."
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