That is unless is defined to exclude in this case, but you will note that Serge requires to be defined on and adherent to (which is essentially that is a limit point of ). So here all is OK.
However there is still a problem:
Now Serge's definition of a limit means does not exist, while the traditional definition has . This is essentially what he is pointing out on page 44 (and at the bottom of that page he does also point out that his convention is different from some other authors - I think I would say than most others myself).