For me, it was the fractional proof that convinced me.
1: 3 * 0.333... = 0.999...
2: 1/3 = 0.333...
3: 3 * 0.333... = 3 * 1/3
4: 0.999... = 1
QED
And yes, 0.333... is rational, as it can be expressed as a ratio of two integers.
This proof is somewhat eye opening. I'm going to have to go and quiz some of the mathematicians I work with about this...should be interesting.
1: 3 * 0.333... = 0.999...
2: 1/3 = 0.333...
3: 3 * 0.333... = 3 * 1/3
4: 0.999... = 1
QED
And yes, 0.333... is rational, as it can be expressed as a ratio of two integers.
This proof is somewhat eye opening. I'm going to have to go and quiz some of the mathematicians I work with about this...should be interesting.