diff --git a/Acme/NumberSystem.hs b/Acme/NumberSystem.hs
--- a/Acme/NumberSystem.hs
+++ b/Acme/NumberSystem.hs
@@ -5,13 +5,14 @@
 import Language.Haskell.TH
 
 type Less = (<=)
+type family Add (m :: Nat) (n :: Nat) :: Nat
 type family Sub (m :: Nat) (n :: Nat) :: Nat
 
 -- | Define the less than relation for numbers up to a number using Template Haskell.
 -- | Also define subtraction.
 -- | E.g. numberSystem 100
 numberSystem :: Integer -> Q [Dec]
-numberSystem theBiggestNumber = return . concat $ lessThan ++ subs
+numberSystem theBiggestNumber = return . concat $ lessThan ++ subs ++ [adds]
   where
     lessThan = map (\i -> map (\j ->
       InstanceD [] (AppT (AppT (ConT (''Less)) (LitT (NumTyLit i))) (LitT (NumTyLit j))) []
@@ -19,3 +20,6 @@
     subs = map (\i -> map (\j ->
       TySynInstD ''Sub [LitT (NumTyLit j), LitT (NumTyLit i)] (LitT (NumTyLit (j - i)))
       ) [i..theBiggestNumber]) [0..theBiggestNumber]
+    adds = map (\i ->
+      TySynInstD ''Add [LitT (NumTyLit i), LitT (NumTyLit 1)] (LitT (NumTyLit (i + 1)))
+      ) [0..theBiggestNumber]
diff --git a/acme-numbersystem.cabal b/acme-numbersystem.cabal
--- a/acme-numbersystem.cabal
+++ b/acme-numbersystem.cabal
@@ -1,7 +1,7 @@
 name:                acme-numbersystem
-version:             0.2.0.0
-synopsis:            Define the less than and subtraction for nats
-description:         Define the less than relation and subtraction for numbers up to a number by using Template Haskell.
+version:             0.3.0.0
+synopsis:            Define the less than and add and subtract for nats
+description:         Define the less than relation, add and subtract for numbers up to a number by using Template Haskell.
 license:             BSD3
 license-file:        LICENSE
 author:              Maxwell Swadling