Vapur's Comments
After reading all these comments, I am still confused about the logic of your hypothesis. You start your argument by stating the equality of two different numbers (0.999... and 1); then, you make a comparison by converting the units to a fraction (1/3, 2/3, and 3/3). Considering that you are using a base 10 number system initially, the representation of the actual number for 1/3 is imperfect and results in an infinite calculation. Changing to the ternary number system can alleviate this issues, but that can introduce other problems when calculating with numbers that aren't easily represented in that system. Depending on the calculation (with fractions versus decimals) it can appear that an infinite number is actually equal to some constant number. The truth of the matter is that 3/3 is equal to 1, while 0.333... multiplied by 3 is equal to 0.999... and not 1. The context is highly important since it changes the precision of your answer.
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x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 1
vs.
x = 0.8
10x = 8.0
10x - x = 8 - 0.8
9x = 7.2
x = 0.8
Therefore, infinite numbers are introducing calculation problems. Infinity minus infinity does not equal zero.