>>> for k in range(10):
...     print(11 * k)
0
11
22
33
44
55
66
77
88
99

					

$$f(11) = 1-1$$ $$f(22) = 2-2$$ $$f(121) = 1-2+1$$

def divisible_by_11(number):
    """Uses above criterion to check if number is divisible by 11"""
    string_number = str(number)
    alternating_sum = sum([(-1) ** i * int(d) for i, d
                           in enumerate(string_number)])
    return alternating_sum == 0
                    

>>> import main
>>> for k in range(11):
...     print(main.divisible_by_11(11 * k))
True
True
True
True
True
True
True
True
True
True

                    

import unittest
import main

class TestDivisible(unittest.TestCase):
    def test_divisible_by_11(self):

        for k in range(10):
            self.assertTrue(main.divisible_by_11(11 * k))
            self.assertFalse(main.divisible_by_11(11 * k + 1))

        # Some more examples
        self.assertTrue(main.divisible_by_11(121))
        self.assertFalse(main.divisible_by_11(123))
                    

$ python3 -m unittest test_main
.
----------------------------------------------------------------------
Ran 1 test in 0.000s
                    

This is how we break mathematics

import unittest
import main

from hypothesis import given
from hypothesis.strategies import integers

class TestDivisible(unittest.TestCase):

    @given(k=integers(min_value=1))
    def test_divisible_by_11(self, k):
        self.assertTrue(main.divisible_by_11(11 * k))
                    

$ python3 -m unittest test_property_main
Falsifying example: test_divisible_by_11(self=, k=19)
F
======================================================================
FAIL: test_divisible_by_11 (test_property_main.TestDivisible)
----------------------------------------------------------------------
Traceback (most recent call last):
  File "test_property_main.py", line 10, in test_divisible_by_11
    def test_divisible_by_11(self, k):
  File "/usr/local/lib/python2.7/site-packages/hypothesis/core.py", line 502, in wrapped_test
    print_example=True, is_final=True
  File "/usr/local/lib/python2.7/site-packages/hypothesis/executors.py", line 57, in default_new_style_executor
    return function(data)
  File "/usr/local/lib/python2.7/site-packages/hypothesis/core.py", line 103, in run
    return test(*args, **kwargs)
  File "test_property_main.py", line 11, in test_divisible_by_11
    self.assertTrue(main.divisible_by_11(11 * k))
AssertionError: False is not true

----------------------------------------------------------------------
Ran 1 test in 0.022s
                    

def divisible_by_11(number):
    """Uses **correct** criterion to check if number is divisible by 11"""
    string_number = str(number)
    alternating_sum = sum([(-1) ** i * int(d) for i, d
                           in enumerate(string_number)])
    return alternating_sum % 11 == 0
                    

Shrinking

hypothesis.readthedocs.org

Property based testing:

Allowing reproducibility of what you have not done yet