What is "transfinite number"

n. (context set theory English) cardinal number 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.

Transfinite numbers are numbers that are " infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite. The term transfinite was coined 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. Few contemporary writers share these qualms; it is now accepted usage to refer to transfinite cardinals and ordinals as "infinite". However, the term "transfinite" also remains in use.