Also, the naive perspective on the .999999999999_=1 debate happens because some people intuit the hyperreals. It's in the hyperreal number system that there can

Also, the naive perspective on the .999999999999_=1 debate happens because some people intuit the hyperreals. It's in the hyperreal number system that there can be an infinitely small difference between .99_ and 1, because that infinitesimal is defined to exist where it isn't defined in the real number system.