Detecting double-spending (long)

[wonderer]

So, this method relies on trusting the bank? After all,
Alice must include her identity in the messages, so that
double spending can be detected later. When the bank 
verifies that it says 'Alice' and not 'Bozo', then it
could keep track of her coins.

Is this true? Is there a way of ever having an ananymous
cash system where the bank does not have to be trusted
at all? What I mean is, where the bank could not possible
know the identities of its customers under any circumstances
where no violation takes place?

Wonderer
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