If we divide time into individual frames, then we would get a set of infinite frames. But what is the cardinality of such a set?
Since time is continuous, like the real numbers, I would expect the cardinality of all frames in time to have the same cardinality as the real numbers.
However, my friend disagrees, and I'm not sure if my logic is good enough. So, would the cardinality of the set of all frames in time be the same as the cardinality of real numbers?
If you begin by stipulating that the time line is a subset of the real numbers, then either the frames themselves are densely ordered (there is no notion of "next frame" available) in which case any infinite cardinality up to that of the continuum is an option (from $\Bbb Q$ to $\Bbb R$).
But I expect that if you use the term "frame" then you can at least move from one frame to another, in which case the time line is a well-ordered (or at least a scattered order) and therefore you can only keep track of countably many frames.
In general the question itself is very vague to give an exact answer, and will depend on too many variables that you haven't addressed: what is the original assumption on the time line, are the frames discrete, do the frames have some positive length (e.g. Planck time is a positive length)? The answer to these questions might change the answer to how many frames can be at all.