I haven't read the entire thing, my barometer for deciding to read the whole thing was the section on limits. The intuition the author tries to develop is very wrong. The whole section on the limit being the smallest impossible number to reach is more misleading than it is instructive. It's dead wrong for probably the most trivial kind of function, the constant functions. If f is a constant function, it's limit (as x approaches any value) is not only not an impossible value for f to obtion, it's the only possible value! Ignoring constant functions, it breaks down with even trivial examples, e.g. the limit of x sin(1/x) as x approaches 0. The limit is 0, but 0 is not impossible to obtain as x approaches 0, in fact f(x) = 0 for infinitely many x in any arbitrarily small neighbourhood of 0.

The real idea is much simpler than "what's the biggest impossible number", it's "what number am I getting closer to."

Also, there wasn't even an example of when a limit doesn't exist, that's quite a significant omission. The function f(x) = sin(1/x) is a good contrast to the previous function; in this case, the limit does not exist as x approaches 0, and it's easy to see here that it's because f(x) doesn't get closer to any value, it keeps oscillating wildly between -1 and 1.