Definition:Subsequential Limit
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Definition
Let $\sequence {x_n}$ be a sequence.
Let $\sequence {x_{n_r} }$ be a subsequence of $\sequence {x_n}$.
Suppose that $\sequence {x_{n_r} }$ converges to a limit $x$.
Then $x$ is called a subsequential limit of $\sequence {x_n}$.
Also see
- First Subsequence Rule
- Limit of Subsequence equals Limit of Sequence
- Divergent Sequence may be Bounded
Sources
- 1953: Walter Rudin: Principles of Mathematical Analysis: $3.5$