I think the author might be conflating sizes of sets and "calculating" with infinity as if it were a number. Sets really can have a cardinality of infinity (an

I think the author might be conflating sizes of sets and "calculating" with infinity as if it were a number. Sets really can have a cardinality of infinity (and beyond). If I have any number of primes, I can construct another prime which is different from all primes I've had before. That makes the total number of primes infinite. On the other hand, you have things like infinite sums, infinite fractions, irrational numbers, etc which appear to require an infinite series of steps to calculate and nevertheless yield a result that we somehow know. That can appear paradoxical and discouraging when learning. I think in those situations, it can help a lot to remember we're really talking about limits: An infinite sum is not an actual sum - rather it's a set of sums which differ only in one parameter, the number of parts that are summed. Each individual sum is perfectly ordinary, but if you put in ever-larger values for the parameter, the results of the individual sums might get ever closer to some particular number - the "result" of the infinite sum.