Basic concepts in infinite set theory | Ordinal numbers | Cardinal numbers

Transfinite number

In mathematics, transfinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite. 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 by Georg Cantor in 1895, who wished to avoid some of the implications of the word infinite in connection with these objects, which were, nevertheless, not finite. Few contemporary writers share these qualms; it is now accepted usage to refer to transfinite cardinals and ordinals as infinite numbers. Nevertheless, the term "transfinite" also remains in use. (Wikipedia).

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Finite set | Beth number | Cardinality of the continuum | Ordinal number | Zermelo–Fraenkel set theory | Ordinal arithmetic | Actual infinity | Dedekind-infinite set | Order type | Natural number | Cardinal number | Mathematics | Continuum hypothesis | Hyperreal number | Real number | Infinity | Infinitesimal | Morse–Kelley set theory | Cardinality | Surreal number