= Solution
The <aleph numbers> enumerate the infinite <initial ordinals> by <transfinite recursion>:
$$
\boxed{\aleph_0=\omega,\qquad\aleph_{\alpha+1}=(\aleph_\alpha)^+,\qquad
\aleph_\lambda=\sup_{\alpha<\lambda}\aleph_\alpha\quad(\lambda\text{ a nonzero limit ordinal}).}
$$
Here $\kappa^+$ is the least cardinal strictly larger than $\kappa$. The <Generalized continuum hypothesis> is
$$
\boxed{2^\kappa=\kappa^+\quad\text{for every infinite cardinal }\kappa,}
$$
equivalently $2^{\aleph_\alpha}=\aleph_{\alpha+1}$ for every <ordinal> $\alpha$ in ZFC.
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