[Merged by Bors] - feat: explicit logarithmic bounds on the harmonic numbers #9984
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Co-authored-by: Michael Stoll <99838730+MichaelStollBayreuth@users.noreply.github.com>
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Prove $\log(n+1) \le H_n \le 1 + \log(n)$ for all natural numbers $n$. There is an existing proof that $H_n$ is not an integer which uses p-adics. Since the new result uses some heavy machinery that is disjoint from the existing proof, the file is split into three parts to keep the dependencies lighter. See [zulip](https://leanprover.zulipchat.com/#narrow/stream/217875-Is-there-code-for-X.3F/topic/basic.20log.20bounds.20on.20harmonic.20sums) Co-authored-by: Arend Mellendijk <FLDutchmann@users.noreply.github.com>
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Prove $\log(n+1) \le H_n \le 1 + \log(n)$ for all natural numbers $n$. There is an existing proof that $H_n$ is not an integer which uses p-adics. Since the new result uses some heavy machinery that is disjoint from the existing proof, the file is split into three parts to keep the dependencies lighter. See [zulip](https://leanprover.zulipchat.com/#narrow/stream/217875-Is-there-code-for-X.3F/topic/basic.20log.20bounds.20on.20harmonic.20sums) Co-authored-by: Arend Mellendijk <FLDutchmann@users.noreply.github.com>
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Prove $\log(n+1) \le H_n \le 1 + \log(n)$ for all natural numbers $n$. There is an existing proof that $H_n$ is not an integer which uses p-adics. Since the new result uses some heavy machinery that is disjoint from the existing proof, the file is split into three parts to keep the dependencies lighter. See [zulip](https://leanprover.zulipchat.com/#narrow/stream/217875-Is-there-code-for-X.3F/topic/basic.20log.20bounds.20on.20harmonic.20sums) Co-authored-by: Arend Mellendijk <FLDutchmann@users.noreply.github.com>
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Prove $\log(n+1) \le H_n \le 1 + \log(n)$ for all natural numbers $n$. There is an existing proof that $H_n$ is not an integer which uses p-adics. Since the new result uses some heavy machinery that is disjoint from the existing proof, the file is split into three parts to keep the dependencies lighter. See [zulip](https://leanprover.zulipchat.com/#narrow/stream/217875-Is-there-code-for-X.3F/topic/basic.20log.20bounds.20on.20harmonic.20sums) Co-authored-by: Arend Mellendijk <FLDutchmann@users.noreply.github.com>
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Prove $\log(n+1) \le H_n \le 1 + \log(n)$ for all natural numbers $n$. There is an existing proof that $H_n$ is not an integer which uses p-adics. Since the new result uses some heavy machinery that is disjoint from the existing proof, the file is split into three parts to keep the dependencies lighter. See [zulip](https://leanprover.zulipchat.com/#narrow/stream/217875-Is-there-code-for-X.3F/topic/basic.20log.20bounds.20on.20harmonic.20sums) Co-authored-by: Arend Mellendijk <FLDutchmann@users.noreply.github.com>
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Prove $\log(n+1) \le H_n \le 1 + \log(n)$ for all natural numbers $n$. There is an existing proof that $H_n$ is not an integer which uses p-adics. Since the new result uses some heavy machinery that is disjoint from the existing proof, the file is split into three parts to keep the dependencies lighter. See [zulip](https://leanprover.zulipchat.com/#narrow/stream/217875-Is-there-code-for-X.3F/topic/basic.20log.20bounds.20on.20harmonic.20sums) Co-authored-by: Arend Mellendijk <FLDutchmann@users.noreply.github.com>
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Prove$\log(n+1) \le H_n \le 1 + \log(n)$ for all natural numbers $n$ .
There is an existing proof that$H_n$ is not an integer which uses p-adics. Since the new result uses some heavy machinery that is disjoint from the existing proof, the file is split into three parts to keep the dependencies lighter.
See zulip