1.实数集不可数.
2.\(Z^+\)的幂集和\(\mathbb{R}\)等势.
3.\(|A|\lt|P(A)|\).（康托定理）
4.\((0,1),[0,1],\mathbb{R}\)等势.
首先证明(0,1)和[0,1]等势
By the Schröder-Bernstein theorem,
it suffices to find one-to-one functions f : (0, 1)→[0, 1]
and g : [0, 1] → (0, 1). Let f (x) = x and g(x) = (x +1)/3.
然后证明(0,1)和R等势
