Basic lemmas about sequences #187
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CohenCyril
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I will start rebasing this branch |
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@ybertot : it is not yet up to mathcomp standards but here is a tentative proof for your information |
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TODO: Hardy's theorem (the true converse of Cesaro)... |
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Definitions: - `[sequence E]_n` is a special notation for `fun n => E` - `series u_` is the sequence of partial sums - `[normed S]` is the series of absolute values, if S is a series - `harmonic` is the name of a sequence, apply `series` to them to get the series. Example: `cvg [normed series (geometric a z)]` states the absolute convergence of the series \sum_(n > 0) |a z^n|. Theorems: - lots of helper lemmas to prove convergence of sequences - convergence of harmonic sequence - convergence of a series implies convergence of a sequence - absolute convergence implies convergence of series Co-Authored-By: Cyril Cohen <cyril.cohen@inria.fr>
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The purpose of this PR is to add a file
sequences.vto gather standard definitions and lemmas about sequences. It certainly deserves to be improved (completed and generalized) but maybe it is worth having it as soon as possible to have a place to share lemmas, e..g, for increasing sequences, and to defer improvements to future PRs (PR #207 is such a PR).There is also a filesequences_examples.vthat defines a few standard sequences and proves a few lemmas about them, mostly as a test bed.