diff --git a/Lib/test/test_math_property.py b/Lib/test/test_math_property.py
new file mode 100644
index 000000000..7d51aa17b
--- /dev/null
+++ b/Lib/test/test_math_property.py
@@ -0,0 +1,41 @@
+import functools
+import unittest
+from math import isnan, nextafter
+from test.support import requires_IEEE_754
+from test.support.hypothesis_helper import hypothesis
+
+floats = hypothesis.strategies.floats
+integers = hypothesis.strategies.integers
+
+
+def assert_equal_float(x, y):
+    assert isnan(x) and isnan(y) or x == y
+
+
+def via_reduce(x, y, steps):
+    return functools.reduce(nextafter, [y] * steps, x)
+
+
+class NextafterTests(unittest.TestCase):
+    @requires_IEEE_754
+    @hypothesis.given(
+        x=floats(),
+        y=floats(),
+        steps=integers(min_value=0, max_value=2**16))
+    def test_count(self, x, y, steps):
+        assert_equal_float(via_reduce(x, y, steps),
+                           nextafter(x, y, steps=steps))
+
+    @requires_IEEE_754
+    @hypothesis.given(
+        x=floats(),
+        y=floats(),
+        a=integers(min_value=0),
+        b=integers(min_value=0))
+    def test_addition_commutes(self, x, y, a, b):
+        first = nextafter(x, y, steps=a)
+        second = nextafter(first, y, steps=b)
+        combined = nextafter(x, y, steps=a+b)
+        hypothesis.note(f"{first} -> {second} == {combined}")
+
+        assert_equal_float(second, combined)