As with finite numbers, there are two ways of thinking of transfinite numbers, as ordinal and cardinal numbers. Unlike the finite ordinals and cardinals, the transfinite ordinals and cardinals define different classes of numbers.

- The lowest transfinite ordinal number is ω.
- The first transfinite cardinal number is aleph-null, , the cardinality of the infinite set of the integers. The next lowest cardinal number is aleph-one, .

In both the cardinal and ordinal number systems, the transfinite numbers can keep on going forever, with progressively more bizarre kinds of number.

Beyond all these, Georg Cantor's conception of the Absolute Infinite surely represents the absolute largest possible concept of "large number".

See also:

- 2 to the power of C
- Large cardinal
- Mahlo cardinals
- Indescribable cardinals
- Infinitesimal