Example 4.7.2.12 (The First Uncountable Cardinal). We say that a cardinal $\kappa $ is uncountable if it is strictly larger than $\aleph _0$. By virtue of Remark 4.7.2.9, there is a smallest uncountable cardinal, which we denote by $\aleph _{1}$. In other words, $\aleph _{1}$ is the successor cardinal $\aleph _0^{+}$.
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