Consider:

```python
class A(object):
    def __init__(self):
        self.r = iter(range(5))
    def __iter__(self):
        return self
    @property
    def next(self):
        return next(self.r)
```

The `next` method is a property, however:

```python
from collections import Iterator
a = A()
isinstance(a, Iterator) # True
next(a) # TypeError: 'int' object is not callable
```