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Topic: .999 =1: True or False? or Both? (Read 3830 times) |
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mikedagr8
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Re: .999 =1: True or False? or Both?
« Reply #25 on: Oct 10th, 2008, 1:58am » |
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on Oct 9th, 2008, 6:24am, KeyBlader01 wrote:
Mikedagr8, Interesting way of putting it. Thanks for sharing.
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No problem. Everyone in one of my maths classes had to find a unique way to show that .999... was equal to 1. This was mine. Hope it was helpful.
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KeyBlader01
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Re: .999 =1: True or False? or Both?
« Reply #26 on: Oct 21st, 2008, 6:24pm » |
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Thanks everyone. I told my Calculus professor about .999...=1 is equal to one and he laughed and said, yeah that's right. He's knows already!! And he made me suffer trying to find all these proofs for this lol. It's because I said .9999=1 first I suppose. But hey, now I know =D
Thanks again!
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rmsgrey
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Re: .999 =1: True or False? or Both?
« Reply #27 on: Oct 22nd, 2008, 12:38pm » |
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on Oct 21st, 2008, 6:24pm, KeyBlader01 wrote:Thanks everyone. I told my Calculus professor about .999...=1 is equal to one and he laughed and said, yeah that's right. He's knows already!! And he made me suffer trying to find all these proofs for this lol. It's because I said .9999=1 first I suppose. But hey, now I know =D
Thanks again! |
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His goal in doing so would probably have been:
1) to determine whether you understood the correct statement or were merely parroting something you'd read and not really understood.
2) to force you to consolidate your understanding of it.
After all this, you're not likely to forget that 0.999...=1, nor to think that .999=1
There's a difference between "knowing" something because someone told you it's true, and knowing it because you have proved it to be true.
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Grimbal
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Re: .999 =1: True or False? or Both?
« Reply #28 on: Oct 22nd, 2008, 2:40pm » |
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on Oct 22nd, 2008, 12:38pm, rmsgrey wrote:| There's a difference between "knowing" something because someone told you it's true, and knowing it because you have proved it to be true. |
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That's true, I read it somewhere on Internet. 
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hamzak
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Re: .999 =1: True or False? or Both?
« Reply #29 on: Nov 25th, 2008, 5:48pm » |
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well for .999 to equal one there must be 11 trailing 9s including the three already there the reason for this is that at that point they are so incredibly close they say .99999999999 = 1 but from my view it is still not 1 it is .99999999999.
hope i could help
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towr
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Re: .999 =1: True or False? or Both?
« Reply #30 on: Nov 26th, 2008, 12:11am » |
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on Nov 25th, 2008, 5:48pm, hamzak wrote:well for .999 to equal one there must be 11 trailing 9s including the three already there the reason for this is that at that point they are so incredibly close they say .99999999999 = 1 but from my view it is still not 1 it is .99999999999.
hope i could help |
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There must be more than just 11 trailing 9's for it to equal 1, there must be an infinity of them.
Then they're not just close to equal, but are equal. Because there is no difference between them at all.
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Wikipedia, Google, Mathworld, Integer sequence DB
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Mickey1
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Re: .999 =1: True or False? or Both?
« Reply #31 on: Mar 11th, 2010, 5:16am » |
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There is only one way to challenge that 0.999... is not equal to 1, namely to deny that 0.999... is a number. It cannot be written down, and such a statement is not illegal.
It is a process to design numbers arbitrarily close to one, so if both 0.999... and 1 exist (and 1 must exist for legal reasons) they must be equal.
0.999... can either be described a limit of a sum where n goes to infinity, or as an endless collection of partial sums, 0.9, 0.99, 0.999 etc.
You have very little choice regarding the limit concept but you could argure that only rational numbers exist (but I don't know why you would do that).
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| « Last Edit: Mar 11th, 2010, 5:17am by Mickey1 » |
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Grimbal
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Re: .999 =1: True or False? or Both?
« Reply #32 on: Mar 12th, 2010, 4:43am » |
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But then, 1/3 = 0.333... doesn't exist either? Or does it?
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