diff --git a/core/math/order/order-docs.factor b/core/math/order/order-docs.factor
index 4c5bc381cc..efce6c3570 100644
--- a/core/math/order/order-docs.factor
+++ b/core/math/order/order-docs.factor
@@ -31,8 +31,7 @@ HELP: +gt+
 { $description "Output by " { $link <=> } " when the first object is strictly greater than the second object." } ;
 
 HELP: invert-comparison
-{ $values { "<=>" symbol }
-          { "<=>'" symbol } }
+{ $values { "<=>" symbol } { ">=<" symbol } }
 { $description "Invert the comparison symbol returned by " { $link <=> } "." }
 { $examples
     { $example "USING: math.order prettyprint ;" "+lt+ invert-comparison ." "+gt+" } } ;
diff --git a/core/math/order/order.factor b/core/math/order/order.factor
index b39b81ba2f..4598d19d35 100644
--- a/core/math/order/order.factor
+++ b/core/math/order/order.factor
@@ -7,7 +7,7 @@ SYMBOL: +lt+
 SYMBOL: +eq+
 SYMBOL: +gt+
 
-: invert-comparison ( <=> -- <=>' )
+: invert-comparison ( <=> -- >=< )
     #! Can't use case, index or nth here
     dup +lt+ eq? [ drop +gt+ ] [ +eq+ eq? +eq+ +lt+ ? ] if ;
 
@@ -19,10 +19,10 @@ GENERIC: <=> ( obj1 obj2 -- <=> )
 
 ! Defining a math generic for comparison forces a single math
 ! promotion, and speeds up comparisons on numbers.
-: (real<=>) ( x y -- ? )
+: (real<=>) ( x y -- <=> )
     2dup < [ 2drop +lt+ ] [ number= +eq+ +gt+ ? ] if ; inline
 
-MATH: real<=> ( x y -- ? )
+MATH: real<=> ( x y -- <=> )
 M: fixnum real<=> { fixnum fixnum } declare (real<=>) ; inline
 M: bignum real<=> { bignum bignum } declare (real<=>) ; inline
 M: float real<=> { float float } declare (real<=>) ; inline