diff --git a/kalk/src/integration_testing.rs b/kalk/src/integration_testing.rs
index 7be5725..d4649a3 100644
--- a/kalk/src/integration_testing.rs
+++ b/kalk/src/integration_testing.rs
@@ -42,6 +42,7 @@ mod tests {
     }
 
     #[test_case("basics")]
+    #[test_case("comparisons")]
     #[test_case("comprehensions")]
     #[test_case("derivation")]
     #[test_case("functions")]
diff --git a/kalk/src/kalk_value/mod.rs b/kalk/src/kalk_value/mod.rs
index b714ebb..3d2bea8 100644
--- a/kalk/src/kalk_value/mod.rs
+++ b/kalk/src/kalk_value/mod.rs
@@ -928,6 +928,9 @@ impl KalkValue {
                     && (imaginary.clone() - imaginary_rhs.clone()).abs()
                         < ACCEPTABLE_COMPARISON_MARGIN,
             ),
+            (KalkValue::Boolean(boolean), KalkValue::Boolean(boolean_rhs)) => {
+                KalkValue::Boolean(boolean == boolean_rhs)
+            }
             (KalkValue::Matrix(rows), KalkValue::Matrix(rows_rhs)) => {
                 let mut matrices_are_equal = true;
                 for (row, row_rhs) in rows.iter().zip(rows_rhs) {
@@ -969,6 +972,9 @@ impl KalkValue {
                     || (imaginary.clone() - imaginary_rhs.clone()).abs()
                         > ACCEPTABLE_COMPARISON_MARGIN,
             ),
+            (KalkValue::Boolean(boolean), KalkValue::Boolean(boolean_rhs)) => {
+                KalkValue::Boolean(boolean != boolean_rhs)
+            }
             (KalkValue::Vector(_), KalkValue::Vector(_))
             | (KalkValue::Matrix(_), KalkValue::Matrix(_)) => {
                 if let KalkValue::Boolean(boolean) = self.eq_without_unit(rhs) {
@@ -1001,7 +1007,7 @@ impl KalkValue {
 
         match (self, rhs) {
             (KalkValue::Number(real, _, _), KalkValue::Number(real_rhs, _, _)) => {
-                KalkValue::Boolean(real.clone() - real_rhs.clone() < ACCEPTABLE_COMPARISON_MARGIN)
+                KalkValue::Boolean(real.clone() - real_rhs.clone() < -ACCEPTABLE_COMPARISON_MARGIN)
             }
             _ => KalkValue::nan(),
         }
diff --git a/kalk/src/parser.rs b/kalk/src/parser.rs
index 5444cce..e944a02 100644
--- a/kalk/src/parser.rs
+++ b/kalk/src/parser.rs
@@ -352,7 +352,7 @@ fn parse_or(context: &mut Context) -> Result<Expr, CalcError> {
 }
 
 fn parse_and(context: &mut Context) -> Result<Expr, CalcError> {
-    let left = parse_equality(context)?;
+    let left = parse_comparison(context)?;
 
     if match_token(context, TokenKind::And) {
         let op = advance(context).kind;
@@ -364,7 +364,7 @@ fn parse_and(context: &mut Context) -> Result<Expr, CalcError> {
     Ok(left)
 }
 
-fn parse_equality(context: &mut Context) -> Result<Expr, CalcError> {
+fn parse_comparison(context: &mut Context) -> Result<Expr, CalcError> {
     let mut left = parse_to(context)?;
 
     // Equality check
@@ -380,10 +380,36 @@ fn parse_equality(context: &mut Context) -> Result<Expr, CalcError> {
         let right = if op == TokenKind::Equals && match_token(context, TokenKind::OpenBrace) {
             parse_piecewise(context)?
         } else {
-            parse_to(context)?
+            parse_comparison(context)?
         };
 
-        left = Expr::Binary(Box::new(left), op, Box::new(right));
+        left = match right {
+            Expr::Binary(
+                inner_left,
+                inner_op
+                @
+                (TokenKind::Equals
+                | TokenKind::NotEquals
+                | TokenKind::GreaterThan
+                | TokenKind::LessThan
+                | TokenKind::GreaterOrEquals
+                | TokenKind::LessOrEquals),
+                inner_right,
+            ) => Expr::Binary(
+                Box::new(Expr::Binary(
+                    Box::new(left),
+                    op,
+                    Box::new(*inner_left.clone()),
+                )),
+                TokenKind::And,
+                Box::new(Expr::Binary(
+                    Box::new(*inner_left),
+                    inner_op,
+                    Box::new(*inner_right),
+                )),
+            ),
+            _ => Expr::Binary(Box::new(left), op, Box::new(right)),
+        }
     }
 
     Ok(left)
diff --git a/tests/comparisons.kalker b/tests/comparisons.kalker
new file mode 100644
index 0000000..7ad0944
--- /dev/null
+++ b/tests/comparisons.kalker
@@ -0,0 +1,13 @@
+x = 2
+true = (1 = 1)
+false = (1 != 1)
+
+(x > 2) = false and
+(x < 2) = false and
+(x = 2) = true and
+(x >= 2) = true and
+(x <= 2) = true and
+(1 < x < 2) = false and
+(x < 3 < 4) = true and
+(1 > x > 2) = false and
+(x > 3 > 4) = false
\ No newline at end of file