this post was submitted on 27 Jun 2024
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x=.9999...
10x=9.9999...
Subtract x from both sides
9x=9
x=1
There it is, folks.
Divide 1 by 3: 1÷3=0.3333...
Multiply the result by 3 reverting the operation: 0.3333... x 3 = 0.9999.... or just 1
0.9999... = 1
In this context, yes, because of the cancellation on the fractions when you recover.
1/3 x 3 = 1
I would say without the context, there is an infinitesimal difference. The approximation solution above essentially ignores the problem which is more of a functional flaw in base 10 than a real number theory issue
This seems to be conflating
0.333...3with0.333...One is infinitesimally close to 1/3, the other is a decimal representation of 1/3. Indeed, if1-0.999...resulted in anything other than 0, that would necessarily be a number with more significant digits than0.999...which would mean that the...failed to be an infinite repetition.