Aleph-1 is the set theory symbol ℵ_1 for the smallest infinite set larger than ℵ_0 (Aleph-0), which in turn is equal to the cardinal number of the set of countable ordinal numbers. The continuum hypothesis asserts that ℵ_1 = c, where c is the cardinal number of the "large" infinite set of real numbers (called the continuum in set theory). However, the truth of the continuum hypothesis depends on the version of set theory you are using and so is undecidable. Curiously enough, n-dimensional space has the same number of points (c) as one-dimensional space, or any finite interval of one-dimensional space (a line segment), as was first recognized by Georg Cantor.

aleph-0 | cardinal number | continuum | continuum hypothesis | countably infinite | finite | infinite | ordinal number | transfinite number | uncountably infinite