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0.999... = 1 (?)

Poll: 0.999... = 1?
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0.999... = 1 (?)
shouri
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#81
2010-03-12, 04:37 PM
Lucida Wrote:Let me rewrite it.
x = 1 + 2 + 4 + 8 + 16 + 32 + ...
2x = 2 + 4 + 8 + 16 + 32 + 64 + ...
x = 1 + (2 + 4 + 8 + 16 + 32 + 64 + ...) = 1 + 2x
x - 1 = 2x To get to the next line you'd have to subtract x on both sides. So you'd get 2x -x which you reduced to x. This does not work when x is something infinitely large. Infinity minus Infinity is undefined, thus the contradiction later.
-1 = x
1 + 4 + 8 + 16 + 32 + ... = -1?

But yes, you're right; the proof is fallacious because divergent series can't be algebraically manipulated like that.
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Messages In This Thread
0.999... = 1 (?) - by Nikkey - 2010-03-11, 06:09 PM
0.999... = 1 (?) - by Link - 2010-03-11, 06:14 PM
0.999... = 1 (?) - by Milelke - 2010-03-11, 06:16 PM
0.999... = 1 (?) - by Horusmaster - 2010-03-11, 06:17 PM
0.999... = 1 (?) - by Corn - 2010-03-11, 06:25 PM
0.999... = 1 (?) - by Kevo - 2010-03-11, 06:31 PM
0.999... = 1 (?) - by Link - 2010-03-11, 06:31 PM
0.999... = 1 (?) - by Horusmaster - 2010-03-11, 06:35 PM
0.999... = 1 (?) - by Nikkey - 2010-03-11, 06:37 PM
0.999... = 1 (?) - by Cyadd - 2010-03-11, 06:37 PM
0.999... = 1 (?) - by Horusmaster - 2010-03-11, 06:45 PM
0.999... = 1 (?) - by Corn - 2010-03-11, 06:46 PM
0.999... = 1 (?) - by shouri - 2010-03-11, 06:59 PM
0.999... = 1 (?) - by Horusmaster - 2010-03-11, 07:00 PM
0.999... = 1 (?) - by Corn - 2010-03-11, 07:03 PM
0.999... = 1 (?) - by shouri - 2010-03-11, 07:05 PM
0.999... = 1 (?) - by Corn - 2010-03-11, 07:06 PM
0.999... = 1 (?) - by Horusmaster - 2010-03-11, 07:06 PM
0.999... = 1 (?) - by Corn - 2010-03-11, 07:08 PM
0.999... = 1 (?) - by Horusmaster - 2010-03-11, 07:11 PM
0.999... = 1 (?) - by Nikkey - 2010-03-11, 07:15 PM
0.999... = 1 (?) - by Corn - 2010-03-11, 07:21 PM
0.999... = 1 (?) - by 2147483647 - 2010-03-11, 07:26 PM
0.999... = 1 (?) - by Nikkey - 2010-03-11, 07:26 PM
0.999... = 1 (?) - by Corn - 2010-03-11, 07:27 PM
0.999... = 1 (?) - by Horusmaster - 2010-03-11, 07:29 PM
0.999... = 1 (?) - by Milelke - 2010-03-11, 07:56 PM
0.999... = 1 (?) - by Horusmaster - 2010-03-11, 08:02 PM
0.999... = 1 (?) - by Corn - 2010-03-11, 08:03 PM
0.999... = 1 (?) - by 2147483647 - 2010-03-11, 08:03 PM
0.999... = 1 (?) - by Khoi - 2010-03-11, 08:04 PM
0.999... = 1 (?) - by randompeep - 2010-03-11, 08:16 PM
0.999... = 1 (?) - by Tikey - 2010-03-11, 08:23 PM
0.999... = 1 (?) - by Milelke - 2010-03-11, 08:25 PM
0.999... = 1 (?) - by Corn - 2010-03-11, 08:26 PM
0.999... = 1 (?) - by Manu - 2010-03-11, 08:37 PM
0.999... = 1 (?) - by Dusk - 2010-03-11, 08:39 PM
0.999... = 1 (?) - by PwNeR88 - 2010-03-11, 08:41 PM
0.999... = 1 (?) - by DarkPwnage - 2010-03-11, 08:43 PM
0.999... = 1 (?) - by Corn - 2010-03-11, 08:43 PM
0.999... = 1 (?) - by Hazzy - 2010-03-11, 08:57 PM
0.999... = 1 (?) - by y0y0y0y0shi0 - 2010-03-11, 08:58 PM
0.999... = 1 (?) - by 2147483647 - 2010-03-11, 09:07 PM
0.999... = 1 (?) - by shouri - 2010-03-11, 09:10 PM
0.999... = 1 (?) - by Tikey - 2010-03-11, 09:11 PM
0.999... = 1 (?) - by Hazzy - 2010-03-11, 09:12 PM
0.999... = 1 (?) - by 2147483647 - 2010-03-11, 09:13 PM
0.999... = 1 (?) - by Khoi - 2010-03-11, 09:15 PM
0.999... = 1 (?) - by shouri - 2010-03-11, 09:21 PM
0.999... = 1 (?) - by 2147483647 - 2010-03-11, 09:23 PM
0.999... = 1 (?) - by shouri - 2010-03-11, 09:25 PM
0.999... = 1 (?) - by Dusk - 2010-03-11, 09:35 PM
0.999... = 1 (?) - by Noah - 2010-03-11, 09:42 PM
0.999... = 1 (?) - by 2147483647 - 2010-03-11, 09:47 PM
0.999... = 1 (?) - by Beaner - 2010-03-11, 10:05 PM
0.999... = 1 (?) - by Hazzy - 2010-03-11, 10:07 PM
0.999... = 1 (?) - by Kalovale - 2010-03-11, 10:09 PM
0.999... = 1 (?) - by Noah - 2010-03-11, 10:09 PM
0.999... = 1 (?) - by Horusmaster - 2010-03-11, 10:10 PM
0.999... = 1 (?) - by 2147483647 - 2010-03-11, 10:23 PM
0.999... = 1 (?) - by Sn1perJohnE - 2010-03-11, 10:40 PM
0.999... = 1 (?) - by Noah - 2010-03-11, 10:55 PM
0.999... = 1 (?) - by Shidoshi - 2010-03-11, 11:02 PM
0.999... = 1 (?) - by Russt - 2010-03-12, 12:28 AM
0.999... = 1 (?) - by 2147483647 - 2010-03-12, 01:29 AM
0.999... = 1 (?) - by Russt - 2010-03-12, 01:39 AM
0.999... = 1 (?) - by 2147483647 - 2010-03-12, 02:00 AM
0.999... = 1 (?) - by Nikkey - 2010-03-12, 02:45 AM
0.999... = 1 (?) - by 2147483647 - 2010-03-12, 02:47 AM
0.999... = 1 (?) - by Fiel - 2010-03-12, 04:55 AM
0.999... = 1 (?) - by Kalovale - 2010-03-12, 05:10 AM
0.999... = 1 (?) - by Russt - 2010-03-12, 12:15 PM
0.999... = 1 (?) - by Horusmaster - 2010-03-12, 12:23 PM
0.999... = 1 (?) - by Russt - 2010-03-12, 12:27 PM
0.999... = 1 (?) - by Khoi - 2010-03-12, 12:32 PM
0.999... = 1 (?) - by Horusmaster - 2010-03-12, 12:39 PM
0.999... = 1 (?) - by Russt - 2010-03-12, 12:57 PM
0.999... = 1 (?) - by Hazzy - 2010-03-12, 02:05 PM
0.999... = 1 (?) - by Russt - 2010-03-12, 02:36 PM
0.999... = 1 (?) - by Nikkey - 2010-03-12, 03:39 PM
0.999... = 1 (?) - by shouri - 2010-03-12, 04:37 PM
0.999... = 1 (?) - by Milelke - 2010-03-12, 09:05 PM
0.999... = 1 (?) - by Hazzy - 2010-03-12, 09:15 PM
0.999... = 1 (?) - by Cancambo - 2010-03-12, 09:26 PM
0.999... = 1 (?) - by Milelke - 2010-03-12, 09:33 PM
0.999... = 1 (?) - by Jellyflower - 2010-03-12, 10:31 PM
0.999... = 1 (?) - by Russt - 2010-03-12, 11:50 PM
0.999... = 1 (?) - by Dusk - 2010-03-13, 12:10 AM
0.999... = 1 (?) - by Kabanaw - 2010-03-13, 12:21 AM
0.999... = 1 (?) - by shouri - 2010-03-13, 02:54 AM
0.999... = 1 (?) - by 2147483647 - 2010-03-13, 04:06 AM
0.999... = 1 (?) - by Locked - 2010-03-13, 06:12 AM
0.999... = 1 (?) - by Noah - 2010-03-13, 08:47 AM
0.999... = 1 (?) - by Fiel - 2010-03-14, 05:12 AM
0.999... = 1 (?) - by 2147483647 - 2010-03-14, 05:46 AM
0.999... = 1 (?) - by Shidoshi - 2010-03-14, 08:36 PM
0.999... = 1 (?) - by GummyBear - 2010-03-15, 05:09 AM
0.999... = 1 (?) - by 2147483647 - 2010-03-18, 02:44 AM
0.999... = 1 (?) - by shouri - 2010-03-18, 03:10 AM
0.999... = 1 (?) - by Dusk - 2010-03-18, 09:25 AM
0.999... = 1 (?) - by Noah - 2010-03-18, 12:59 PM
0.999... = 1 (?) - by Jellyflower - 2010-03-24, 11:30 AM
0.999... = 1 (?) - by shouri - 2010-03-24, 04:01 PM

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