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0.999... = 1 (?)

Poll: 0.999... = 1?
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0.999... = 1 (?)
shouri
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#99
2010-03-18, 03:10 AM
2147483647 Wrote:Sorry for reviving this thread, but I'm baffled by this. My Calculus teacher, a Ph.D. in Mathematics, told me today that the closed set [0,1) has no upper bound. Specifically, I asked him the question, "what is the highest possible number that can fit in that set"? He replied,"there is no highest number". Then I proposed that the highest number might be 0.999...9! and he replied that it isn't, because it equals 1, and that trumps the definition of the closed set.

=[

That's because he wasn't correct when he stated that .999999..... is in the open set [0,1).

.99999..... is 1. It's not in [0,1)



Also, what definition of upper bound do you guys have 0.o

In real analysis, an upper bound is any number bigger than or equal to everything in the set. So any number bigger than 1 is an upper bound for both [0,1] and [0,1).

The least upper bound would be the minimum of all upper bounds. Which in both cases would be 1.
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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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