feat(analysis/specific_limits/complex) #18887
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Specific limits complex numbers Prerequisite for upcoming Hadamard Three Lines Theorem. Separate from basic to avoid adding dependencies. Proof of lemma by Patrick Massot
Louddy
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I'm surprised we can't state this more generally; is it true for any ℝ-algebra? |
Added a lemma for the limit of `1/n` into an `ℝ` algebra.
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Simplified proofs in term of ℝ algebras
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Why do you remove the TODO comment on the following lemma? I don't think this lemma solves that problem -- the point of the comment is that it would be nice to cover topological rings which aren't algebras over the reals. |
Re-added the TODO
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My mistake! |
eric-wieser
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I've created a zulip thread about this PR. |
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I left a comment in the Zulip thread with a |
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This PR introduces a single new lemma about the limit of 1 / n as n → ∞ in the complex numbers. It has been placed in a new file for two reasons: the obvious file to put it (analysis/specific_limits/basic) does not have the required imports, and it also makes porting easier since basic has already been ported to mathlib4.
Note that this is a prerequisite for an upcoming PR for the Hadamard three-line theorem.
Finally, thanks to Patrick Massot for supplying the actual proof on Zulip a while back!