hash values and equality

[Ethan Furman]

Several folk have said that objects that compare equal must hash equal, 
and the docs also state this 
http://docs.python.org/dev/reference/datamodel.html#object.__hash__

I'm hoping somebody can tell me what horrible thing will happen if this 
isn't the case?  Here's a toy example of a class I'm thinking of writing 
that will compare equal with int's, but hash differently:

--> class Wierd():
...     def __init__(self, value):
...         self.value = value
...     def __eq__(self, other):
...         return self.value == other
...     def __hash__(self):
...         return hash((self.value + 13) ** 3)
...
--> one = Wierd(1)
--> two = Wierd(2)
--> three = Wierd(3)
--> one
<Wierd object at 0x00BFE710>
--> one == 1
True
--> one == 2
False
--> two == 2
True
--> three == 3
True
--> d = dict()
--> d[one] = '1'
--> d[two] = '2'
--> d[three] = '3'
--> d
{<Wierd object at 0x00BFE710>: '1',
  <Wierd object at 0x00BFE870>: '3',
  <Wierd object at 0x00BFE830>: '2'}
--> d[1] = '1.0'
--> d[2] = '2.0'
--> d[3] = '3.0'
--> d
{<Wierd object at 0x00BFE870>: '3',
  1: '1.0',
  2: '2.0',
  3: '3.0',
  <Wierd object at 0x00BFE830>: '2',
  <Wierd object at 0x00BFE710>: '1'}
--> d[2]
'2.0'
--> d[two]
'2'

All information greatly appreciated!

~Ethan~