`Rung`

definition

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module: IndisputableMonolith.Support.RungFractions
domain: Support
line: 22 · github
papers citing: none yet

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IndisputableMonolith.Support.RungFractions on GitHub at line 22.

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formal source

  19namespace RungFractions
  20
  21/-- A (possibly fractional) rung on the φ‑ladder. -/
  22abbrev Rung := ℚ
  23
  24/-- Embed an integer rung into a rational rung. -/
  25@[simp] def ofInt (z : ℤ) : Rung := (z : ℚ)
  26
  27/-- The quarter‑ladder embedding: `k ↦ k/4`. -/
  28@[simp] def quarter (k : ℤ) : Rung := (k : ℚ) / 4
  29
  30/-- The half‑ladder embedding: `k ↦ k/2`. -/
  31@[simp] def half (k : ℤ) : Rung := (k : ℚ) / 2
  32
  33/-- Convert a rational rung to a real exponent (for `Real.rpow`). -/
  34@[simp] def toReal (r : Rung) : ℝ := (r : ℝ)
  35
  36theorem quarter_eq (k : ℤ) : quarter k = (k : ℚ) / 4 := rfl
  37theorem half_eq (k : ℤ) : half k = (k : ℚ) / 2 := rfl
  38
  39end RungFractions
  40end Support
  41end IndisputableMonolith

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