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0.999... = 1 (?)

Poll: 0.999... = 1?
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0.999... = 1 (?)
Corn
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#5
2010-03-11, 06:25 PM (This post was last modified: 2010-03-11, 06:31 PM by Corn.)
They have some faulty premises.

"For any two different real numbers, you can pick a third number which is between them."

Who said that?

If the difference between two numbers is zero, then they are equal. For example, 5 - 5 = 0 because 5 = 5.

The difference between 1.0000... and 0.9999... is:

1.0000... - 0.9999... = 0.0000...
= 0

Therefore, they are equal.


Their arguement is bs. Sure, "..." might mean going on forever, but 1.0000... - 0.9999... = 0.0000(keep on going) until 1. This applies to the 3rd problem, too.

A sequence can only have one limit.

Observe that the limit of the sequence

0.9
0.99
0.999
0.9999
0.99999
...
is

0.9999...
That is, the sequence gets closer and closer to 0.9999..., in fact, infinitely close.

But the sequence also gets closer and closer to 1.0000..., in fact, infinitely close. So 1.0000... is a limit of this sequence too.

But a sequence can only have one limit, so 0.9999... and 1.0000... must be the same.

Isn't 0.99999... equal to 0.9999...?

The rest of his arguements are logical, but I still disagree due to my trig. teacher saying 0.999... approaches 1, but never gets there, and she had this entire complicated proof and crap.
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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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