Comment by lcrz

So the authors tries to be rigorous, but again falls into the same traps that the people who claim 0.9… != 1 fall.

“0.999… = 1 - infinitesimal”

But this is simply not true. Only then they get back to a true statement:

“Inequality between two reals can be stated this way: if you subtract a from b, the result must be a nonzero real number c”.

This post doesn’t clear things up, nor is it mathematically rigorous.

Pointing towards hyperreals is another red herring, because again there 0.999… equals 1.