Theorems · Theorem · real analysis
Real.ofDigits_const_last_eq_one
∀ (b : ℕ) [NeZero b], (Real.ofDigits fun x => Fin.last b) = 1
A generalization of the identity 0.(9) = 1 to arbitrary positional numeral systems.
- Defined in
- Mathlib.Analysis.Real.OfDigits
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
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
- Norm.normproof · cited by 5,413
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- SummationFilter.unconditionalproof · cited by 2,068
- Nat.cast_zeroproof · cited by 1,870
- absproof · cited by 1,814
- le_of_ltproof · cited by 1,175
- tsumproof · cited by 1,148
- one_ne_zeroproof · cited by 885
- ne_of_gtproof · cited by 637
Cited by1
Results whose statement or proof uses this declaration.
- Real.ofDigits_const_last_eq_one'proof · cited by 1