Originally Posted by

**drewmandan**
No one said that number equals one. We said 0.9~ equals one. See, the way you wrote your version of the number, it's obvious that you think the 9's "end". They don't. As soon as you understand that, you will see that it clearly is 1.

Also, here's something to consider.

1/3 *in base 10* is 0.3~

1/3 *in base 6* is 0.2000~ (in other words, just 0.2. Do the long division if you don't believe me)

Then, in base 6, if you do 3 * 0.2, you get 1.

This would suggest that there's no fundamental difference between numbers with an infinite number of non-zero repeating decimals and an infinite number of zeros. Therefore, it would seem that the "1/3 proof" is, in fact, quite valid.