0.999... / 3 = 0.333... 1 / 3 = 0.333... Ergo 1 = 0.999...

(Or see algebraic proof by @Valthorn@feddit.nu)

If the difference between two numbers is so infinitesimally small they are in essence mathematically equal, then I see no reason to not address then as such.

If you tried to make a plank of wood 0.999...m long (and had the tools to do so), you'd soon find out the universe won't let you arbitrarily go on to infinity. You'd find that when you got to the planck length, you'd have to either round up the previous digit, resolving to 1, or stop at the last 9.

The way I see it is the difference between equal numbers is zero.

The difference between 0.999… and 1 is 0.000…, and since the nines don't end, the zeros don't end, so the difference is just zero.

Meaning 0.999… = 1