diff --git a/README.md b/README.md
index b13cbda4..29533f3a 100644
--- a/README.md
+++ b/README.md
@@ -438,14 +438,6 @@ In jq, division by 0 yields an error, whereas
 in jaq, `n / 0` yields `nan` if `n == 0`, `infinite` if `n > 0`, and `-infinite` if `n < 0`.
 jaq's behaviour is closer to the IEEE standard for floating-point arithmetic (IEEE 754).
 
-jaq implements a total ordering on floating-point numbers to allow sorting values.
-Therefore, it unfortunately has to enforce that `nan == nan`.
-(jq gets around this by enforcing that `nan < nan` is true, yet `nan > nan` is false,
-which breaks basic laws about total orders.)
-
-Like jq, jaq prints `nan` and `infinite` as `null` in JSON,
-because JSON does not support encoding these values as numbers.
-
 
 ## Assignments
 
diff --git a/jaq-json/src/lib.rs b/jaq-json/src/lib.rs
index fdeadea7..863eb7de 100644
--- a/jaq-json/src/lib.rs
+++ b/jaq-json/src/lib.rs
@@ -889,7 +889,14 @@ fn float_eq(left: f64, right: f64) -> bool {
 
 fn float_cmp(left: f64, right: f64) -> Ordering {
     if left == 0. && right == 0. {
+        // consider negative and positive 0 as equal
         Ordering::Equal
+    } else if left.is_nan() && right.is_nan() {
+        // there are more than 50 shades of NaN, and which of these
+        // you strike when you perform a calculation is not deterministic (!),
+        // therefore `total_cmp` may yield different results for the same calculation
+        // so we bite the bullet and handle this like in jq
+        Ordering::Less
     } else {
         f64::total_cmp(&left, &right)
     }
diff --git a/jaq-std/src/defs.jq b/jaq-std/src/defs.jq
index cf4a3e4b..a1989a82 100644
--- a/jaq-std/src/defs.jq
+++ b/jaq-std/src/defs.jq
@@ -21,7 +21,7 @@ def isobject:  . >= {};
 # Numbers
 def nan:      0 / 0;
 def infinite: 1 / 0;
-def isnan:      . == nan;
+def isnan:      . < nan and nan < .;
 def isinfinite: . == infinite or  . == -infinite;
 def isfinite:   isnumber and (isinfinite | not);
 def isnormal:   isnumber and ((. == 0 or isnan or isinfinite) | not);
diff --git a/jaq-std/tests/defs.rs b/jaq-std/tests/defs.rs
index cc9e08e9..3452db4d 100644
--- a/jaq-std/tests/defs.rs
+++ b/jaq-std/tests/defs.rs
@@ -32,7 +32,7 @@ yields!(tofromdate, "946684800 | todate | fromdate", 946684800);
 
 yields!(
     drem_nan,
-    "[drem(nan, 1; nan, 1)] == [nan, nan, nan, 0.0]",
+    "[drem(nan, 1; nan, 1)] | (.[0:-1] | all(isnan)) and .[-1] == 0.0",
     true
 );
 yields!(
@@ -237,7 +237,7 @@ yields!(
 );
 yields!(
     scalb_nan,
-    "[scalb(nan, 1; nan, 1)] == [nan, nan, nan, 2.0]",
+    "[scalb(nan, 1; nan, 1)] | (.[0:-1] | all(isnan)) and .[-1] == 2.0",
     true
 );
 yields!(