MDMAlliance said:
Zkuq said:
MDMAlliance said:
Really, the hole I see is that if it eventually did hit one, there should also be an objective point where the switch happened. I can also see why 0.999... is looked at "since it goes on forever, and there cannot be a number between 0.999... and 1, 0.999... has to be 1." I understand that. That doesn't change the fact that it isn't a fixed object in my perspective. Infinity would have to be a fixed object, too.
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Do you think 0.999... is a number at all? Nope. If you think it is, then it is definitely a fixed object. There's also a difference between an infinite number of periods and infinity. I do acknowledge their differences, but there are many ways where they function the same way. Also, what do you have against the proof using the sum of a geometric series? Can you tell where it goes wrong? If it goes wrong somewhere, you can point out the exact spot where the error is and you can do it without geometric intuition. I simply do not think that the equation is perfect, especially considering what its limitations are. I have not taken math in over 3 years so I would really need to study this stuff and come back to it later in order to produce any realistic conclusions.
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How do you even compare 0.999... and 1 if you don't think 0.999... is a number? How do you compare two entirely different things? What is it if it's not a number?
And finally: Have you ever tried deriving the sum for geometric series? First you do it for the first n terms which is fairly easy, then you take the limit n->infinity which is almost trivial in this case. The equation is perfect, there's no denying that. The steps required to derive the equation aren't high-level mathematics, they're fairly simple.
