Move things around, add more to fields (#16)

Numbers/Reals.agda

@@ -0,0 +1,32 @@
+{-# OPTIONS --safe --warning=error #-}
+
+open import Fields
+open import Rings
+open import Functions
+open import Orders
+open import LogicalFormulae
+open import Rationals
+open import Naturals
+
+open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
+
+module Reals where
+  record Subset {m n : _} (A : Set m) (B : Set n) : Set (m ⊔ n) where
+    field
+      inj : A → B
+      injInj : Injection inj
+
+  --record RealField {n : _} {A : Set n} {R : Ring A} {F : Field R} : Set _ where
+  --  field
+  --    orderedField : OrderedField F
+  --  open OrderedField orderedField
+  --  open TotalOrder ord
+  --  open Ring R
+  --  field
+  --    complete : {c : _} {C : Set c} → (S : Subset C A) → (upperBound : A) → ({s : C} → (Subset.inj S s) < upperBound) → Sg A (λ lub → ({s : C} → (Subset.inj S s) < lub) && ({s : C} → (Subset.inj S s) < upperBound → (Subset.inj S s) < lub))
+
+
+  record Real : Set where
+    field
+      f : ℕ → ℚ
+      converges : {ε : ℚ} → Sg ℕ (λ x → {y : ℕ} → x <N y → (f x) +Q (f y) <Q ε)