diff --git a/library/data/prod.lean b/library/data/prod.lean
index 71ba33247..8644c36c8 100644
--- a/library/data/prod.lean
+++ b/library/data/prod.lean
@@ -26,8 +26,8 @@ namespace prod
 
   definition pr1 (p : prod A B) := rec (λ x y, x) p
   definition pr2 (p : prod A B) := rec (λ x y, y) p
-  notation `pr₁`:max := pr1
-  notation `pr₂`:max := pr2
+  notation `pr₁` := pr1
+  notation `pr₂` := pr2
 
   variables (a : A) (b : B)
 
diff --git a/library/data/unit.lean b/library/data/unit.lean
index 3de08a28f..fad608890 100644
--- a/library/data/unit.lean
+++ b/library/data/unit.lean
@@ -7,7 +7,7 @@ open decidable
 inductive unit : Type :=
   star : unit
 namespace unit
-  notation `⋆`:max := star
+  notation `⋆` := star
 
   -- remove duplication?
   protected theorem equal (a b : unit) : a = b :=
diff --git a/library/general_notation.lean b/library/general_notation.lean
index 79df60cb6..efd27d26f 100644
--- a/library/general_notation.lean
+++ b/library/general_notation.lean
@@ -40,9 +40,6 @@ precedence `▸`:75      -- infixr
 
 -- ### types and type constructors
 
-precedence `ℕ`:max
-precedence `ℤ`:max
-
 precedence `⊎`:25      -- infixr
 precedence `×`:30      -- infixr
 
@@ -69,7 +66,6 @@ precedence `||`:65     -- infixl
 -- ### set operations
 
 precedence `∈`:50
-precedence `∅`:max
 precedence `∩`:70
 precedence `∪`:65
 
diff --git a/library/type.lean b/library/type.lean
index ab6325ccb..52b45248d 100644
--- a/library/type.lean
+++ b/library/type.lean
@@ -2,9 +2,9 @@
 -- Released under Apache 2.0 license as described in the file LICENSE.
 -- Authors: Leonardo de Moura
 
-notation `Prop`:max  := Type.{0}
-notation `Type'`:max := Type.{_+1}
-notation `Type₊`:max := Type.{_+1}
-notation `Type₁`:max := Type.{1}
-notation `Type₂`:max := Type.{2}
-notation `Type₃`:max := Type.{3}
+notation `Prop`  := Type.{0}
+notation `Type'` := Type.{_+1}
+notation `Type₊` := Type.{_+1}
+notation `Type₁` := Type.{1}
+notation `Type₂` := Type.{2}
+notation `Type₃` := Type.{3}