= Solution
A <strongly inaccessible cardinal> is an uncountable <cardinal> $\lambda$ that is both regular and a strong limit:
$$
\boxed{\operatorname{cf}(\lambda)=\lambda,\qquad
2^\mu<\lambda\text{ for every cardinal }\mu<\lambda.}
$$
Regularity excludes expressing $\lambda$ as the supremum of a shorter increasing sequence, while the strong-limit requirement concerns all smaller <power sets>. Merely being an uncountable regular limit <cardinal> is the weaker notion of a <weakly inaccessible cardinal>.
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