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Move towards base-n expansions (#112)

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Patrick Stevens
2020-04-11 19:46:26 +01:00
committed by GitHub
parent e9aa1bcc05
commit 380548134d
22 changed files with 312 additions and 102 deletions
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7
Fields/CauchyCompletion/Definition.agda
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@@ -27,9 +27,12 @@ open Group additiveGroup
open Field F
open import Rings.Orders.Total.Lemmas order
open import Rings.Orders.Total.Cauchy order
open import Groups.Lemmas additiveGroup
cauchy : Sequence A → Set (m ⊔ o)
cauchy s = ∀ (ε : A) → (0R < ε) → Sg ℕ (λ N → ∀ {m n : ℕ} → (N <N m) → (N <N n) → abs ((index s m) -R (index s n)) < ε)
cauchyWellDefined : {s1 s2 : Sequence A} → ((m : ℕ) → index s1 m ∼ index s2 m) → cauchy s1 → cauchy s2
cauchyWellDefined {s1} {s2} prop c e 0<e with c e 0<e
... | N , pr = N , λ {m} {n} N<m N<n → <WellDefined (absWellDefined _ _ (+WellDefined (prop m) (inverseWellDefined (prop n)))) reflexive (pr N<m N<n)
record CauchyCompletion : Set (m ⊔ o) where
field