applicability: $\mathbb {N, Z, Q, R, C}$
Let \((a_n)_{n\in\mathbb N}\) be a real sequence and let $(n_k)_{k\in\mathbb N}$ be a strictly monotonically increasing sequence of natural numbers \(n_k\in\mathbb N\), i.e. $$n_0 < n_1 < n_2 < \ldots$$ Then the sequence \[(a_{n_k})_{k\in\mathbb N}\] is called the real subsequence (or just subsequence) of \((a_n)_{n\in\mathbb N}\).
Definitions: 1
Proofs: 2 3 4
Propositions: 5
Theorems: 6
