Theorems · Theorem · real analysis
Real.ofDigits_eq_sum_add_ofDigits
∀ {b : ℕ} (a : ℕ → Fin b) (n : ℕ),
Real.ofDigits a = ∑ i ∈ Finset.range n, Real.ofDigitsTerm a i + (↑b ^ n)⁻¹ * Real.ofDigits fun i => a (i + n)- Defined in
- Mathlib.Analysis.Real.OfDigits
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- TopologicalSpaceproof · cited by 24,529
- AddCommMonoidproof · cited by 12,281
- Finset.sumstatement and proof · cited by 5,195
- SummationFilter.unconditionalproof · cited by 2,068
- Finset.rangestatement and proof · cited by 1,341
- tsumproof · cited by 1,148
- SummationFilterproof · cited by 607
- Real.ofDigitsTermstatement and proof · cited by 15
- Real.ofDigitsstatement · cited by 14
- Summable.tsum_mul_leftproof · cited by 8
- Summable.sum_add_tsum_nat_addproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- ofDigits_zero_two_sequence_mem_cantorSetproof · cited by 2
- ofDigits_zero_two_sequence_uniqueproof · cited by 0
- Real.abs_ofDigits_sub_ofDigits_leproof · cited by 0