Theorems · Theorem · number theory
Real.convergent_succ
∀ (ξ : ℝ) (n : ℕ), ξ.convergent (n + 1) = ↑⌊ξ⌋ + ((Int.fract ξ)⁻¹.convergent n)⁻¹
The (n+1)th convergent of ξ is the nth convergent of 1/(fract ξ).
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Int.floorstatement · cited by 225
- Int.fractstatement · cited by 114
- Real.convergentstatement · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- Real.convs_eq_convergentproof · cited by 1
- Real.exists_rat_eq_convergent'proof · cited by 1