diff --git a/data-interval.cabal b/data-interval.cabal
--- a/data-interval.cabal
+++ b/data-interval.cabal
@@ -1,5 +1,5 @@
 Name:		data-interval
-Version:	1.0.0
+Version:	1.0.1
 License:	BSD3
 License-File:	COPYING
 Author:		Masahiro Sakai (masahiro.sakai@gmail.com)
diff --git a/src/Data/Interval.hs b/src/Data/Interval.hs
--- a/src/Data/Interval.hs
+++ b/src/Data/Interval.hs
@@ -50,13 +50,15 @@
   , upperBound'
   , width
 
-  -- * Comparison operators
-  , (<!), (<=!), (==!), (>=!), (>!)
-  , (<?), (<=?), (==?), (>=?), (>?)
+  -- * Universal comparison operators
+  , (<!), (<=!), (==!), (>=!), (>!), (/=!)
 
-  -- * Comparison operators that produce witnesses (experimental)
-  , (<??), (<=??), (==??), (>=??), (>??)
+  -- * Existential comparison operators
+  , (<?), (<=?), (==?), (>=?), (>?), (/=?)
 
+  -- * Existential comparison operators that produce witnesses (experimental)
+  , (<??), (<=??), (==??), (>=??), (>??), (/=??)
+
   -- * Combine
   , intersection
   , intersections
@@ -81,26 +83,38 @@
 import Data.Ratio
 import Prelude hiding (null)
 
--- | Interval
+-- | The intervals (/i.e./ connected and convex subsets) over real numbers __R__.
 data Interval r = Interval !(EndPoint r, Bool) !(EndPoint r, Bool)
   deriving (Eq, Typeable)  
 
--- | Lower bound of the interval
-lowerBound :: Num r => Interval r -> EndPoint r
+-- | Lower endpoint (/i.e./ greatest lower bound)  of the interval.
+--
+-- * 'lowerBound' of the empty interval is 'PosInf'.
+--
+-- * 'lowerBound' of a left unbounded interval is 'NegInf'.
+--
+-- * 'lowerBound' of an interval may or may not be a member of the interval.
+lowerBound :: Interval r -> EndPoint r
 lowerBound (Interval (lb,_) _) = lb
 
--- | Upper bound of the interval
-upperBound :: Num r => Interval r -> EndPoint r
+-- | Upper endpoint (/i.e./ least upper bound) of the interval.
+--
+-- * 'upperBound' of the empty interval is 'NegInf'.
+--
+-- * 'upperBound' of a right unbounded interval is 'PosInf'.
+-- 
+-- * 'upperBound' of an interval may or may not be a member of the interval.
+upperBound :: Interval r -> EndPoint r
 upperBound (Interval _ (ub,_)) = ub
 
--- | Lower bound of the interval and whether it is included in the interval.
+-- | 'lowerBound' of the interval and whether it is included in the interval.
 -- The result is convenient to use as an argument for 'interval'.
-lowerBound' :: Num r => Interval r -> (EndPoint r, Bool)
+lowerBound' :: Interval r -> (EndPoint r, Bool)
 lowerBound' (Interval lb _) = lb
 
--- | Upper bound of the interval and whether it is included in the interval.
+-- | 'upperBound' of the interval and whether it is included in the interval.
 -- The result is convenient to use as an argument for 'interval'.
-upperBound' :: Num r => Interval r -> (EndPoint r, Bool)
+upperBound' :: Interval r -> (EndPoint r, Bool)
 upperBound' (Interval _ ub) = ub
 
 instance NFData r => NFData (Interval r) where
@@ -235,6 +249,8 @@
       )
 
 -- | intersection of a list of intervals.
+--
+-- Since 0.6.0
 intersections :: (Ord r, Num r) => [Interval r] -> Interval r
 intersections xs = foldl' intersection whole xs
 
@@ -263,6 +279,8 @@
       )
 
 -- | convex hull of a list of intervals.
+--
+-- Since 0.6.0
 hulls :: (Ord r, Num r) => [Interval r] -> Interval r
 hulls xs = foldl' hull empty xs
 
@@ -274,6 +292,10 @@
     LT -> False
     GT -> True
 
+isSingleton :: Ord r => Interval r -> Bool
+isSingleton (Interval (Finite l, True) (Finite u, True)) = l==u
+isSingleton _ = False
+
 -- | Is the element in the interval?
 member :: Ord r => r -> Interval r -> Bool
 member x (Interval (x1,in1) (x2,in2)) = condLB && condUB
@@ -286,7 +308,7 @@
 notMember a i = not $ member a i
 
 -- | Is this a subset?
--- @(i1 `isSubsetOf` i2)@ tells whether @i1@ is a subset of @i2@.
+-- @(i1 \``isSubsetOf`\` i2)@ tells whether @i1@ is a subset of @i2@.
 isSubsetOf :: Ord r => Interval r -> Interval r -> Bool
 isSubsetOf (Interval lb1 ub1) (Interval lb2 ub2) = testLB lb1 lb2 && testUB ub1 ub2
   where
@@ -301,7 +323,7 @@
         GT -> False
         EQ -> not in1 || in2 -- in1 => in2
 
--- | Is this a proper subset? (ie. a subset but not equal).
+-- | Is this a proper subset? (/i.e./ a subset but not equal).
 isProperSubsetOf :: Ord r => Interval r -> Interval r -> Bool
 isProperSubsetOf i1 i2 = i1 /= i2 && i1 `isSubsetOf` i2
 
@@ -324,6 +346,7 @@
 pickup _ = Nothing
 
 -- | 'simplestRationalWithin' returns the simplest rational number within the interval.
+-- 
 -- A rational number @y@ is said to be /simpler/ than another @y'@ if
 --
 -- * @'abs' ('numerator' y) <= 'abs' ('numerator' y')@, and
@@ -332,6 +355,7 @@
 -- 
 -- (see also 'approxRational')
 --
+-- Since 0.4.0
 simplestRationalWithin :: RealFrac r => Interval r -> Maybe Rational
 simplestRationalWithin i | null i = Nothing
 simplestRationalWithin i 
@@ -354,7 +378,7 @@
         condLB = if in1 then x1 <= Finite x' else x1 < Finite x'
         condUB = if in2 then Finite x' <= x2 else Finite x' < x2
 
--- | For all @x@ in @X@, @y@ in @Y@. @x '<' y@
+-- | For all @x@ in @X@, @y@ in @Y@. @x '<' y@?
 (<!) :: Real r => Interval r -> Interval r -> Bool
 a <! b =
   case ub_a `compare` lb_b of
@@ -369,19 +393,25 @@
     (ub_a, in1) = upperBound' a
     (lb_b, in2) = lowerBound' b
 
--- | For all @x@ in @X@, @y@ in @Y@. @x '<=' y@
+-- | For all @x@ in @X@, @y@ in @Y@. @x '<=' y@?
 (<=!) :: Real r => Interval r -> Interval r -> Bool
 a <=! b = upperBound a <= lowerBound b
 
--- | For all @x@ in @X@, @y@ in @Y@. @x '==' y@
+-- | For all @x@ in @X@, @y@ in @Y@. @x '==' y@?
 (==!) :: Real r => Interval r -> Interval r -> Bool
 a ==! b = a <=! b && a >=! b
 
--- | For all @x@ in @X@, @y@ in @Y@. @x '>=' y@
+-- | For all @x@ in @X@, @y@ in @Y@. @x '/=' y@?
+--
+-- Since 1.0.1
+(/=!) :: Real r => Interval r -> Interval r -> Bool
+a /=! b = null $ a `intersection` b
+
+-- | For all @x@ in @X@, @y@ in @Y@. @x '>=' y@?
 (>=!) :: Real r => Interval r -> Interval r -> Bool
 (>=!) = flip (<=!)
 
--- | For all @x@ in @X@, @y@ in @Y@. @x '>' y@
+-- | For all @x@ in @X@, @y@ in @Y@. @x '>' y@?
 (>!) :: Real r => Interval r -> Interval r -> Bool
 (>!) = flip (<!)
 
@@ -393,6 +423,8 @@
     ub_b = upperBound b
 
 -- | Does there exist an @x@ in @X@, @y@ in @Y@ such that @x '<' y@?
+--
+-- Since 1.0.0
 (<??) :: (Real r, Fractional r) => Interval r -> Interval r -> Maybe (r,r)
 a <?? b = do
   guard $ lowerBound a < upperBound b
@@ -425,6 +457,8 @@
     (ub_b, in2) = upperBound' b
 
 -- | Does there exist an @x@ in @X@, @y@ in @Y@ such that @x '<=' y@?
+-- 
+-- Since 1.0.0
 (<=??) :: (Real r, Fractional r) => Interval r -> Interval r -> Maybe (r,r)
 a <=?? b　= do
   case pickup (intersection a b) of
@@ -436,15 +470,42 @@
       return (x,y)
 
 -- | Does there exist an @x@ in @X@, @y@ in @Y@ such that @x '==' y@?
+-- 
+-- Since 1.0.0
 (==?) :: Real r => Interval r -> Interval r -> Bool
 a ==? b = not $ null $ intersection a b
 
 -- | Does there exist an @x@ in @X@, @y@ in @Y@ such that @x '==' y@?
+--
+-- Since 1.0.0
 (==??) :: (Real r, Fractional r) => Interval r -> Interval r -> Maybe (r,r)
 a ==?? b = do
   x <- pickup (intersection a b)
   return (x,x)
 
+-- | Does there exist an @x@ in @X@, @y@ in @Y@ such that @x '/=' y@?
+--
+-- Since 1.0.1
+(/=?) :: Real r => Interval r -> Interval r -> Bool
+a /=? b = not (null a) && not (null b) && not (a == b && isSingleton a)
+
+-- | Does there exist an @x@ in @X@, @y@ in @Y@ such that @x '/=' y@?
+--
+-- Since 1.0.1
+(/=??) :: (Real r, Fractional r) => Interval r -> Interval r -> Maybe (r,r)
+a /=?? b = do
+  guard $ not $ null a
+  guard $ not $ null b
+  guard $ not $ a == b && isSingleton a
+  if not (isSingleton b)
+    then f a b
+    else liftM (\(y,x) -> (x,y)) $ f b a
+  where
+    f a b = do
+      x <- pickup a
+      y <- msum [pickup (b `intersection` c) | c <- [NegInf <..< Finite x, Finite x <..< PosInf]]
+      return (x,y)
+
 -- | Does there exist an @x@ in @X@, @y@ in @Y@ such that @x '>=' y@?
 (>=?) :: Real r => Interval r -> Interval r -> Bool
 (>=?) = flip (<=?)
@@ -454,10 +515,14 @@
 (>?) = flip (<?)
 
 -- | Does there exist an @x@ in @X@, @y@ in @Y@ such that @x '>=' y@?
+--
+-- Since 1.0.0
 (>=??) :: (Real r, Fractional r) => Interval r -> Interval r -> Maybe (r,r)
 (>=??) = flip (<=??)
 
 -- | Does there exist an @x@ in @X@, @y@ in @Y@ such that @x '>' y@?
+--
+-- Since 1.0.0
 (>??) :: (Real r, Fractional r) => Interval r -> Interval r -> Maybe (r,r)
 (>??) = flip (<??)
 
diff --git a/test/TestInterval.hs b/test/TestInterval.hs
--- a/test/TestInterval.hs
+++ b/test/TestInterval.hs
@@ -10,7 +10,12 @@
 import Test.Framework.Providers.HUnit
 import Test.Framework.Providers.QuickCheck2
 
-import Data.Interval (Interval, Extended (..), (<=..<=), (<=..<), (<..<=), (<..<), (<!), (<=!), (==!), (>=!), (>!), (<?), (<=?), (==?), (>=?), (>?), (<??), (<=??), (==??), (>=??), (>??))
+import Data.Interval
+  ( Interval, Extended (..), (<=..<=), (<=..<), (<..<=), (<..<)
+  , (<!), (<=!), (==!), (>=!), (>!), (/=!)
+  , (<?), (<=?), (==?), (>=?), (>?), (/=?)
+  , (<??), (<=??), (==??), (>=??), (>??), (/=??)
+  )
 import qualified Data.Interval as Interval
 
 {--------------------------------------------------------------------
@@ -320,6 +325,9 @@
 prop_le_some_refl =
   forAll intervals $ \a -> not (Interval.null a) ==> a <=? a
 
+prop_ne_all_not_refl =
+  forAll intervals $ \a -> not (Interval.null a) ==> not (a /=! a)
+
 prop_lt_all_singleton =
   forAll arbitrary $ \a ->
   forAll arbitrary $ \b ->
@@ -342,6 +350,15 @@
   forAll arbitrary $ \a ->
     Interval.singleton (a::Rational) ==! Interval.singleton a
 
+prop_ne_all_singleton =
+  forAll arbitrary $ \a ->
+  forAll arbitrary $ \b ->
+    (a::Rational) /= b ==> Interval.singleton a /=! Interval.singleton b
+
+prop_ne_all_singleton_2 =
+  forAll arbitrary $ \a ->
+    not $ Interval.singleton (a::Rational) /=! Interval.singleton a
+
 prop_lt_some_singleton =
   forAll arbitrary $ \a ->
   forAll arbitrary $ \b ->
@@ -379,6 +396,9 @@
 prop_eq_all_empty =
   forAll intervals $ \a -> a ==! Interval.empty
 
+prop_ne_all_empty =
+  forAll intervals $ \a -> a /=! Interval.empty
+
 prop_lt_some_empty =
   forAll intervals $ \a -> not (a <? Interval.empty)
 
@@ -436,6 +456,17 @@
       Just (x,y) ->
         Interval.member x a .&&. Interval.member y b .&&. x == y
 
+prop_ne_some_witness =
+  forAll intervals $ \a ->
+  forAll intervals $ \b ->
+    case a /=?? b of
+      Nothing ->
+        forAll arbitrary $ \x ->
+        forAll arbitrary $ \y ->
+          not (Interval.member x a && Interval.member y b && x /= y)
+      Just (x,y) ->
+        Interval.member x a .&&. Interval.member y b .&&. x /= y
+
 prop_le_some_witness_forget =
   forAll intervals $ \a ->
   forAll intervals $ \b ->
@@ -450,6 +481,11 @@
   forAll intervals $ \a ->
   forAll intervals $ \b ->
     isJust (a ==?? b) == (a ==? b)
+
+prop_ne_some_witness_forget =
+  forAll intervals $ \a ->
+  forAll intervals $ \b ->
+    isJust (a /=?? b) == (a /=? b)
 
 {--------------------------------------------------------------------
   Num