Definition:Subsequence/Warning
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Definition
In the definition of a subsequence, the constraint that $\sequence {n_r}$ be strictly increasing is important.
Thus, for example, $x_3, x_1, x_4, x_2, x_9, x_5 \ldots$ is not a subsequence of $\sequence {x_n}$.
Sources
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 5$: Subsequences: $\S 5.1$: Subsequences