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Fix upperseq definition in Example_6_4_9 #472

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Fix upperseq definition in Example_6_4_9 #472

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2e62081
Fix upperseq definition in Example_6_4_9
Shaunticlair Mar 27, 2026
8b6261b
Update example limsup reference in Section 6.4
Shaunticlair Mar 27, 2026
7975da7
Additional Ex numbering fixes
Shaunticlair Mar 27, 2026
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8 changes: 4 additions & 4 deletions analysis/Analysis/Section_6_4.lean
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Expand Up @@ -119,7 +119,7 @@ example : Example_6_4_8.liminf = ⊥ := by sorry
noncomputable abbrev Example_6_4_9 : Sequence :=
(fun (n:ℕ) ↦ if Even n then (n+1:ℝ)⁻¹ else -(n+1:ℝ)⁻¹)

example (n:ℕ) : Example_6_4_9.upperseq n = if Even n then (n+1:ℝ)⁻¹ else -(n+2:ℝ)⁻¹ := by sorry
example (n:ℕ) : Example_6_4_9.upperseq n = if Even n then (n+1:ℝ)⁻¹ else (n+2:ℝ)⁻¹ := by sorry

example : Example_6_4_9.limsup = 0 := by sorry

Expand All @@ -131,11 +131,11 @@ noncomputable abbrev Example_6_4_10 : Sequence := (fun (n:ℕ) ↦ (n+1:ℝ))

example (n:ℕ) : Example_6_4_10.upperseq n = ⊤ := by sorry

example : Example_6_4_9.limsup = ⊤ := by sorry
example : Example_6_4_10.limsup = ⊤ := by sorry

example (n:ℕ) : Example_6_4_9.lowerseq n = n+1 := by sorry
example (n:ℕ) : Example_6_4_10.lowerseq n = n+1 := by sorry

example : Example_6_4_9.liminf = ⊤ := by sorry
example : Example_6_4_10.liminf = ⊤ := by sorry

/-- Proposition 6.4.12(a) -/
theorem Sequence.gt_limsup_bounds {a:Sequence} {x:EReal} (h: x > a.limsup) :
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