Does 0.999999.... equal 1?

[kickazz]

Say there is a line from A to B

If you move in the direction of point A to point B and cover half the distance each time, you never get to B because it is always possible to divide any number by 2.

You never get to B and the distance gained is 0.99999 ........

Quantum physics suggests you will either stop all together or you will make it to B.

But the same could be said about 0.3333333 not quite ever equaling one third. But if you use the construct of infinity, and assume there are infinite 3s after that decimal point (which is what a recurring decimal is) then it by definition does equal one third. It's just that the base 10 number system doesn't have a nice way of representing that number with a finite number of digits.

0.999999..... is then the same as 0.333333333....... if 0.3 recurring is one third, then
0.9 recurring is three thirds.