Also, she says that in calculus you deal with "infinities 2 levels deeper than" countably infinite (around 4:00). I assume that she means with this the cardinality beth-2, which is 2^c (where c is the continuum), but how often do you deal with that when doing calculus? I think never. There are c real numbers, c continuous functions, c differentiable functions, c complex numbers, c open subsets of R^n. What thing has cardinality 2^c when doing calculus?
When typing this up, I was thinking how many topologies there are on an infinite set X. Is it 2^(|X|) or 2^(2^(|X|))?