Transfinite number

There are two kinds of transfinite numbers, ordinal and cardinal.

The lowest transfinite number ordinal number is ω.

The first transfinite cardinal number is aleph-null[?], the cardinality of the infinite set of the integers. The next highest cardinal number is aleph-one[?].

The continuum hypothesis states that there are no intermediate cardinal numbers between aleph-null and the cardinality of the real numbers (the "continuum"): that is to say, that aleph-one is the same as the cardinality of the real numbers.

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:

• large cardinal[?]
• Mahlo cardinals
• Indescribable cardinals[?]
• infinitesimal