I've wracked my brains a bit on the subject, and I left it at about this point:
* Repeated doubling one after the other can never produce an uncountable infinity: you can always count these since there are a finite (or countable) number produced at each stage
* Repeated doubling backwards, as using the stack, doesn't seem well-defined. If at each (backwards) time t, there are twice as many counters as at t+1, then you could say that a set of counters numbered 0.(0..0
t+1)x become counters numbered 0.(0..0
t)x, but I can't see any way of specifying what the set of potential x is, the definition is consistent with any set defined by the tails of x.
* It's not in principle impossible. There could in theory have been a card that says "do x ... for each legal target", which for a spell which can target any number of creatures, with an infinite number of creatures, would target every possible subset. That card would not play well, it would be crazy even for finite numbers, but it would be eminently possible.
* I can't think of any way to achieve an uncountable. I considered and discarded a few ideas:
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