diff --git a/src/infinite/comparison.jl b/src/infinite/comparison.jl
index b324490..ab76e28 100644
--- a/src/infinite/comparison.jl
+++ b/src/infinite/comparison.jl
@@ -5,6 +5,8 @@ Base.isinf(x::Infinite) = true
 Base.iszero(::Infinite) = false
 
 Base.:(==)(x::Infinite, y::Infinite) = x.signbit == y.signbit
+Base.:(==)(x::Infinite, y::Real) = isinf(y) && signbit(x) == signbit(y)
+Base.:(==)(x::Real, y::Infinite) = y == x
 
 Base.hash(x::Infinite, h::UInt) = hash(isposinf(x) ? Inf : -Inf, h)
 
diff --git a/test/infextendedreal.jl b/test/infextendedreal.jl
index 0aacf88..a490f20 100644
--- a/test/infextendedreal.jl
+++ b/test/infextendedreal.jl
@@ -118,6 +118,7 @@
         @test InfExtendedReal(5) == 5
         @test InfExtendedReal(7) == 7.0
         @test InfExtendedReal(4) != InfExtendedReal(1)
+        @test InfExtendedReal(Inf) == InfExtendedReal(∞)
 
         @test hash(InfExtendedReal(3)) == hash(3)
 
diff --git a/test/infinite.jl b/test/infinite.jl
index 36785c0..493eb0f 100644
--- a/test/infinite.jl
+++ b/test/infinite.jl
@@ -59,7 +59,11 @@
         @test !iszero(x)
         @test !iszero(-x)
         @test x == x
+        @test x == Inf
+        @test Inf == x
         @test x != -x
+        @test x != -Inf
+        @test Inf != -x
         @test hash(x) != hash(-x)
         @test -x < x
         @test x > -x