The key is then that 0.999… means the limit of the infinite sequence, NOT the infinite sequence itself. This makes one question if one even understand such basic things as what a number such as 1 even mean in the real numbers mathematically (you can express it as 1.000…). Importantly then 0.999… IS 1.000… . The same way that 0.500… + 0.500.. IS 1.000… . It don’t BECOME 1.000… . Therefore it’s not two different numbers.