Theorems · Theorem · real analysis
Real.continuousAt_logb_iff
∀ {b x : ℝ}, 0 < b → b ≠ 1 → (ContinuousAt (Real.logb b) x ↔ x ≠ 0)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- ContinuousAtstatement and proof · cited by 697
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- Filter.Tendsto.mono_leftproof · cited by 125
- Real.logbstatement and proof · cited by 119
- ContinuousAt.tendstoproof · cited by 103
- lt_or_gt_of_neproof · cited by 41
- not_tendsto_nhds_of_tendsto_atTopproof · cited by 7
- not_tendsto_nhds_of_tendsto_atBotproof · cited by 3
- Real.continuousAt_logbproof · cited by 2
- Real.tendsto_logb_nhdsNE_zeroproof · cited by 1
- Real.tendsto_logb_nhdsNE_zero_of_base_lt_oneproof · cited by 1
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