>>You will certainly agree that any single finite value xn of a continuous >>quantity x is per se completely irrelevant because it is surrounded by >>infinitely many nearly identical neighbours. > > > No, I will not ...
I am curious about your own arguments.
> >Also, there is intuitively nothing in between (-a, 0) and (0, a). > > Who cares? A variable in (-a, 0) will never become 0, and a variable in (0, a) > neither - and that's important.
Elsewhere I tried to explain that mathematics unites counting of entities with a slightly contradicting geometrical notion. Claiming importance of the first aspect, mathematicans like you violate practical relevance of the latter. I would rather recommend accepting the fundamental discrepancy.