Terry J. Reedy <tjre...@udel.edu> added the comment:

Proposing an expansion of the definition of product() is a *completely* 
different issue from the validity of count() as an input. I answered correctly 
given the current definition of product(): it is not valid input. It is also 
not valid input to your proposed revision:
>>> tuple(itertools.cycle(enumerate(it)) for it in itertools.count())
...
TypeError: 'int' object is not iterable
-- just as I said.

If you want to propose an enhancement, either open an new, enhancement issue or 
post to python-ideas. Since new features can only go in 3.3+, post 3.x code, 
not 2.x. And please do not quibble about the difference between 'infinite' and 
'too large to fit in memory'.

----------
stage:  -> committed/rejected
versions: +Python 3.3 -Python 3.1

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