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0.999...
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| Joss Weatherby |
http://en.wikipedia.org/wiki/0.999
Argued with a couple people about this today. Basically the idea is that in a real number system 0.9999999 with 9 extending for infinity, is equal to 1. They are the same number.
I understand the mathematical concept with real numbers, but I prefer the infinitesimal number system when it comes to this. I feel it is far more logical to assume that 0.999... never reaches 1, it just infinitely gets closer and closer, but never becomes 1. This I think is far more representative of physical world realities.
Any math people have any opinion on this? |
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| OurManFlint |
I like the geometric series example when it comes to this. Basically
0.999...= 9/10 + (9/10)^2 + (9/10)^3 + .... = 9(1/10) / (1-(1/10)) = 1.
So 0.999... converges to 1. For all intents and purposes, any use of the real number system would use this, and would not treat both numbers as different. |
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| LAdazeNYnights |
.333 + .666 = .999
1/3 + 2/3 = 3/3 = 1
you can't explain that.
science. |
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| Taipan |
| quote: | Originally posted by LAdazeNYnights
.333 + .666 = .999
1/3 + 2/3 = 3/3 = 1
you can't explain that.
science. |
/thread. |
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| Joss Weatherby |
| so what is 0.999...+0.999...? |
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| Meat187 |
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| Blake |
I might not have believed you a semester or so ago. The logicians who make up these rules are nuts :p
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| aquila |
| quote: | Originally posted by LAdazeNYnights
.333 + .666 = .999
1/3 + 2/3 = 3/3 = 1
you can't explain that.
science. |
0.333 != 1/3
0.666 != 2/3 |
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| Taipan |
| quote: | Originally posted by Joss Weatherby
so what is 0.999...+0.999...? |
1.999999999999 or 2 |
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| Zharen |
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| Marcus Summers |
| I stopped caring about numbers once I got an accountant. |
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| LAdazeNYnights |
| quote: | Originally posted by aquila
0.333 != 1/3
0.666 != 2/3 |
.3bar, or .3repeating = 1/3
.6bar, etc = 2/3
.9bar /= 3/3
techmology is wack |
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