This is in large part due to the difficulty with reasoning about infinite representations. You do have to add axioms to your system to be able to reason about 0

This is in large part due to the difficulty with reasoning about infinite representations. You do have to add axioms to your system to be able to reason about 0.9999... Stating that 0.9999... = 1 without exposing these new tools meant to grapple with concepts that physically cannot be grappled with is a huge mistake.