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 Posted: Sun Aug 27, 2006 7:44 pm
Ok, just by my flawed thinking I came upon this conclusion when speaking of our existance in retrospect to the grand sceme. I said that .0000000000000000000000000000~(infinite)1 = 0.
Just as .99999999999999999999999999999999~9 = 1.
Is this false?
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Posted: Sun Aug 27, 2006 7:52 pm
Endert Ok, just by my flawed thinking I came upon this conclusion when speaking of our existance in retrospect to the grand sceme. I said that .0000000000000000000000000000~(infinite)1 = 0. Just as .99999999999999999999999999999999~9 = 1. Is this false? I think it's true, because if you take the limit of the function at infinity, it's zero. the function itself approaches zero, same for the second funciton which approaches one, that is if we model the value using a function.
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Posted: Sun Aug 27, 2006 8:00 pm
Ok, I was just making sure because all I used was logic and sometimes thats not enough. Wierd how we aren't taught about that in school mabeys its implied when they teach about .9999999...
Ha poweroutage got to it before the ED people did, thats funny.
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Posted: Sun Aug 27, 2006 10:03 pm
Endert Ok, I was just making sure because all I used was logic and sometimes thats not enough. Wierd how we aren't taught about that in school mabeys its implied when they teach about .9999999... Ha poweroutage got to it before the ED people did, thats funny. yeah I didn't learn that in school either. funny thing. the phys&mat guild is your filter kiddo, one, quality response (don't quote me if I end up being wrong though, things like that always bite me in the a**).
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Posted: Mon Aug 28, 2006 3:27 am
They don't teach it in high school because it's somewhat badly worded.
You aren't going to come across the expression 0.000...(infinite)1 other than in this exact question. Mostly because you're not supposed to stick things on the end of infinite sequences. That would imply there is a "beyond" the infinity, which only works in some number systems, the reals not being one of them.
You can always do the trick of 0.00000...1 * 10 = 0.00000...1, and the only real number that can be multiplied by 10 and return itself is 0, so therefore 0.0000....1 must be equal to 0. Unfortunately, that assumes that 0.0000...1 gives a valid real number, and your teachers don't want to deal with that (because they probably can't). .999999... is easy to justify, because you can get it as the product of two real numbers, but .000...1 isn't quite the same. You can very well say that it's too small to be a real number, in which case the difference between 1 and .9999... is not a real number and thus there is no difference.
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Posted: Mon Aug 28, 2006 10:26 am
The problem with such expressions is their interpretation. It would be more correct to say that "0.000...1" with implicit infinite number of zeros before the 1 is not a well-formed expression, and thus does not represent any number at all. As such, it is neither true nor false, but simply without meaning.
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Posted: Mon Aug 28, 2006 3:46 pm
"Not even wrong," Vorpal?
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Posted: Mon Aug 28, 2006 5:28 pm
Swordmaster Dragon "Not even wrong," Vorpal? Exactly!
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Posted: Tue Aug 29, 2006 12:19 am
Speaking of which, have you read Peter Woit's novel of the same name - a critique of string theory - or its review in Seed? Oh, and as if to drive the point home...
shameless plug for Seed magazine
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