| JRPGfan said:
What Im saying is 0.9999999 = 1 is wrong. Why? Because you would always be missing that 0.000000001 part. You can tell their not the same number on each side, by the fact that we re writeing them differntly.
In concept.... because we live in a physical world, where theres a limit to things, it could make practical sense. However in math terms I think its wrong.
I think the proof is bad math. I just dont know how to proove that its bad math. |
The reason it seems like something is "missing" is because you're thinking of it like it's finite. Infinity doesn't work the same way. There is no missing piece, because, as soon as you try to subtract that "missing piece" from 1, you've made it a finite number, and your subtraction won't result in 0.999.... Your subtraction will result in a number that is finite. Infinity is just really weird, and not at all intuitive. For example: most people think that there is nothing bigger than infinity, but there are actually some infinities that are bigger than others (they're called different levels of infinity), and this leads to things like the fact that there are the same "number" of positive integers as there are positive AND negative integers combined, but there are "more" irrational numbers than there are positive and negative integers. Trying to use intuition just doesn't work, because all of our intuition is based on finite things, since, as you said, most of our experience is finite.
However, that doesnt' mean that infinity doesn't exist in a physical world. There are plenty of ways in which infinity manifests itself in a physical world. Time is probably the most common; there is also the age old problem of continuously traveling half the distance to a destination (if you always travel half the remaining distance, it will take you an infinite amount of steps to get there).
