well the suggestion being made is that an infinite series can be terminated - and with a different digit. That's finite right? :) Irrespective of 1/3 = 0.333 (

well the suggestion being made is that an infinite series can be terminated - and with a different digit. That's finite right? :) Irrespective of 1/3 = 0.333 (which can be proven mathematically) terminating an infinite series is impossible. The same fallacy persists in all his other points. For example when he does the 10x business and points out there are still only 5 9's then his series is clearly finite and not infinite - and therefore no longer 0.9 recurring. The main issue with people "disbelieving" 0.9 recurring equals 1 is a misunderstanding of what infinity actually is :) EDIT: in reply to your edit - you've fallen for the misunderstanding of infinite. No one can dispute that 0.3<lots of 3's>3 + 0.0<losts of 0's>1 = 1. But in an infinite series you never get to that 1. The number is 0 (this can be mathematically proven I am told; but it is beyond my ability to do so)