 The cardinal 2ℵ0 is important since it is the size of the continuum (the set of real numbers). Cantor's famous continuum hypothesis (CH) is the statement that 2ℵ0 = ℵ1. This is a special case of the generalized continuum hypothesis (GCH) which asserts that for all α, 2ℵα = ℵα+1. One virtue of GCH is that it gives a complete solution to the problem of computing κλ for infinite cardinals: Assuming GCH, if κ ≤ λ then κλ = λ+; if cf(κ) ≤ λ ≤ κ then κλ = κ+; and if λ &lt; cf(κ) then κλ = κ. 