[Merged by Bors] - refactor(analysis/specific_limits): prove 0 < r → (1+r)^n→∞ for semirings
#2935
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* Add `add_one_pow_unbounded_of_pos` and `tendsto_add_one_pow_at_top_at_top_of_pos` assuming `[linear_ordered_semiring α]` `[archimedean α]`. * Rename `tendsto_pow_at_top_at_top_of_gt_1` to `tendsto_pow_at_top_at_top_of_one_lt`, generalize to an archimedean ordered ring. * Rename `tendsto_pow_at_top_at_top_of_gt_1_nat` to `nat.tendsto_pow_at_top_at_top_of_one_lt`.
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r^n→∞ for semirings(1+r)^n→∞, r > 0 for semirings
urkud
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(1+r)^n→∞, r > 0 for semirings0 < r → (1+r)^n→∞ for semirings
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…irings (#2935) * Add `add_one_pow_unbounded_of_pos` and `tendsto_add_one_pow_at_top_at_top_of_pos` assuming `[linear_ordered_semiring α]` `[archimedean α]`. * Rename `tendsto_pow_at_top_at_top_of_gt_1` to `tendsto_pow_at_top_at_top_of_one_lt`, generalize to an archimedean ordered ring. * Rename `tendsto_pow_at_top_at_top_of_gt_1_nat` to `nat.tendsto_pow_at_top_at_top_of_one_lt`.
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0 < r → (1+r)^n→∞ for semirings0 < r → (1+r)^n→∞ for semirings
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…irings (leanprover-community#2935) * Add `add_one_pow_unbounded_of_pos` and `tendsto_add_one_pow_at_top_at_top_of_pos` assuming `[linear_ordered_semiring α]` `[archimedean α]`. * Rename `tendsto_pow_at_top_at_top_of_gt_1` to `tendsto_pow_at_top_at_top_of_one_lt`, generalize to an archimedean ordered ring. * Rename `tendsto_pow_at_top_at_top_of_gt_1_nat` to `nat.tendsto_pow_at_top_at_top_of_one_lt`.
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add_one_pow_unbounded_of_posandtendsto_add_one_pow_at_top_at_top_of_posassuming[linear_ordered_semiring α][archimedean α].tendsto_pow_at_top_at_top_of_gt_1totendsto_pow_at_top_at_top_of_one_lt, generalize to an archimedeanordered ring.
tendsto_pow_at_top_at_top_of_gt_1_nattonat.tendsto_pow_at_top_at_top_of_one_lt.