> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/200-set-theory/topics/transfinite-number.md). # Transfinite number * Transfinite numbers are numbers that are *infinite*, in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite * **Transfinite cardinals** are used to quantify the size of infinite sets * **Transfinite ordinals** are used to provide an ordering of infinite sets * The term "transfinite" was coined by Georg Cantor in 1915, who wished to avoid some of the implications of the word infinite in connection with these objects, which were, nevertheless, not finite. Nowadays, the term stays but they may be referred to as infinite numbers as well. * ℵ first transfinite cardinal * ℶ second transfinite cardinal * ℷ third transfinite cardinal * ℸ fourth transfinite cardinal