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.^[1][2] The term transfinite was coined in 1895 by Georg Cantor,^[3][4][5][6] who wished to avoid some of the implications of the word infinite in connection with these objects, which were, nevertheless, not finite.^{[citation needed]} 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.

Notable work on transfinite numbers was done by Wacław Sierpiński: Leçons sur les nombres transfinis (1928 book) much expanded into Cardinal and Ordinal Numbers (1958,^[7] 2nd ed. 1965^[8]).