It is known that convergent sequences approximate certain numbers. For example, the sequence $\dfrac12,\dfrac12+\dfrac14, \dfrac12+\dfrac14+\dfrac18,\cdots$ etc approximates the number $1$. Are there sequences that approximate sequences? In other words, some global operation would be applied to the sequence as a whole at each stage, thereby taking it closer and closer to the final sequence. Each term would therefore be a sequence rather than just a number as in the above example.
2026-05-05 05:47:05.1777960025
Sequences approximating sequences
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Yes. That's part of the field of Functional Analysis. Within this field of Mathematics, the sequence spaces are studied.