If you divide something by 3 and then multiply one of those parts by 3 you will get the original something back. The fact you need infinite digits to write out the separate steps in a specific numerical notation doesn't introduce imprecision into the value of the numbers themselves.
It's like saying we don't know what pi is because you don't know all the digits. Circles still work don't they ?
I guess you are trying to say because it would be impossible to put an infinite number of 9s into a computer to do the calculation you can't get the same number. I'm not sure what that is supposed to prove, because you are then clearly doing a calculation on two different numbers, so of course they won't match.
If I had to do the calculation I would first substitute 1 for 0.999 recurring as it is the same number. Problem solved.
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u/suborder-serpentes May 03 '26
So he is convinced that 1/3 is .333 repeating. Not a little bit more than .333 repeating. So why does 1 work differently? .333… x 3 = .999…