>>> class AppendOnUnequal(object):
...     def __init__(self, append_to):
...         self.append_to = append_to
...     def __eq__(self, other):
...         if self is other:
...             return True
...         self.append_to.append(self)
...         return False
... 
>>> L = [1]; AppendOnUnequal(L) in L
True
>>> L = [1]; L.count(AppendOnUnequal(L))
1
>>> L = [1]; L.remove(AppendOnUnequal(L))
>>> L = [1]; L.index(AppendOnUnequal(L))
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: <__main__.AppendOnUnequal object at 0x7f2562d071d0> is not in list


.index() is the only odd one out here. Looks like a bug to me.

This is a non-guaranteed behavior.  It is allowed to be different from other list methods.  The behavior is also very old, stable, and has not been a problem in practice.  No good would come from changing it.

This is because list.index() has start and stop parameters, and L.index(x) is equivalent to L.index(x, 0, len(L)). In list.count() and list.remove() the limit is dynamic during iteration, but in list.index() it is specified by arguments before iterating. It is possible to make the limit static in list.count() and list.remove() or to make it floating if stop is absent or negative in list.index(), but this will complicate and slow down the code without good reason. I suggest to close this issue as "wont fix".