>>11837399I'm sure this has been pointed out before, and if it hasn't you are all really stupid but if n equals .999… then 9n equal 8.999999 not 9. 10n – n equals 9n AND 9.99.. minus .999… equals 9 but 9n cannot be equal to 9 unless you add the condition that .999… is equal to one, which is exactly what you are trying to prove because
If n =.9999… then 9n equals 8.9999… not 9.
Therefore, this is the fallacy of circumlocution. 9n can only equal 9 IFF n equals one, and not if n = .999 which you are trying to prove.
This is the case with every "proof" of .999... equal to 1.
The one where you say
1/3 + 1/3 +1/3 equals 1 does the same thing.
It uses the definition of .3333... equal to 1/3 to make the proof. You have to accept the conclusion to make the conclusion. That is circumlocution: you use the result that a repeating decimal equals a constant to prove the result.
This once again shows why my philosophy degree beats your STEM hands down every time.
