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Author
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Topic: 0.99999~ = 1 ?
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cavediver
Member (Idle past 3670 days) Posts: 4129 From: UK Joined: 06-16-2005
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Message 2 of 237 (543079)
01-15-2010 8:42 AM
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Reply to: Message 1 by Huntard
01-15-2010 8:19 AM
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It is my understanding that 0.9999~ does indeed equal 1. Yes, indeed it does... unless you happen to be a constructivist, that is!
| This message is a reply to: | | | Message 1 by Huntard, posted 01-15-2010 8:19 AM | | Huntard has not replied |
| Replies to this message: | | | Message 3 by Briterican, posted 01-15-2010 8:49 AM | | cavediver has not replied |
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cavediver
Member (Idle past 3670 days) Posts: 4129 From: UK Joined: 06-16-2005
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Message 25 of 237 (543204)
01-16-2010 5:20 AM
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Reply to: Message 18 by Son Goku
01-15-2010 8:35 PM
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Re: Funny Properties
Finally and strangest of all, irrational numbers are more common than rational numbers. More common... And in other news, Graham's Number is quite big 
| This message is a reply to: | | | Message 18 by Son Goku, posted 01-15-2010 8:35 PM | | Son Goku has replied |
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cavediver
Member (Idle past 3670 days) Posts: 4129 From: UK Joined: 06-16-2005
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Message 26 of 237 (543206)
01-16-2010 5:28 AM
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Reply to: Message 23 by Huntard
01-16-2010 4:08 AM
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Re: 1 and NOT 1
No, it's like saying: "I went to Constantinople" and "I went to Istanbul". They're both the same place, just different ways of writing them. I can't believe* it falls to me to raise (again - see my first post in this thread) that this identity is non-existent in finitism, and much of constructivism in general. All the mathematicians here are assuming that infinite decimals such as 0.9999~ actually exist. This is not a trivial point. *I hate constructivism, and wouldn't even mention it other than in derision - except that everyone seems to be assuming it doesn't exist, and it should be brought up for completeness. A very good friend of mine is a finitist, and it generally means we have very little to say to each other mathemtaically! His taste in music is also crap
| This message is a reply to: | | | Message 23 by Huntard, posted 01-16-2010 4:08 AM | | Huntard has not replied |
| Replies to this message: | | | Message 37 by Son Goku, posted 01-16-2010 12:27 PM | | cavediver has not replied |
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cavediver
Member (Idle past 3670 days) Posts: 4129 From: UK Joined: 06-16-2005
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Message 30 of 237 (543219)
01-16-2010 9:42 AM
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Reply to: Message 27 by Dr Jack
01-16-2010 7:22 AM
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Re: 1 and NOT 1
Nope, they're completely the same, philosophically and otherwise. I have to disagree here for the reasons I gave above.
| This message is a reply to: | | | Message 27 by Dr Jack, posted 01-16-2010 7:22 AM | | Dr Jack has replied |
| Replies to this message: | | | Message 31 by Dr Jack, posted 01-16-2010 10:06 AM | | cavediver has replied |
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cavediver
Member (Idle past 3670 days) Posts: 4129 From: UK Joined: 06-16-2005
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Message 32 of 237 (543222)
01-16-2010 10:14 AM
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Reply to: Message 31 by Dr Jack
01-16-2010 10:06 AM
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Re: 1 and NOT 1
Yeah, but finitism is silly. I'll not disagree Edited by cavediver, : No reason given.
| This message is a reply to: | | | Message 31 by Dr Jack, posted 01-16-2010 10:06 AM | | Dr Jack has seen this message but not replied |
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cavediver
Member (Idle past 3670 days) Posts: 4129 From: UK Joined: 06-16-2005
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Message 33 of 237 (543223)
01-16-2010 10:22 AM
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Reply to: Message 28 by Huntard
01-16-2010 8:17 AM
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Re: Funny Properties
Ah yes. Even if every digit were the size of only 1 planck volume, the observable universe would still not be big enough to contain a digital representation of it It's far worse than that! Let's say that for each Planck volume, you are given another entire universe!! And for each Planck volume in that universe, you are given *another* universe!! You would still not have enough Planck volumes to even begin to write out Graham's number 
| This message is a reply to: | | | Message 28 by Huntard, posted 01-16-2010 8:17 AM | | Huntard has not replied |
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cavediver
Member (Idle past 3670 days) Posts: 4129 From: UK Joined: 06-16-2005
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Message 109 of 237 (544178)
01-24-2010 3:03 PM
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Reply to: Message 87 by Jon
01-23-2010 7:27 PM
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Re: Totally right!
I await your modification to your proof And I await your ability to understand SG's argument, but I guess I'll be waiting a long long time...
Your logic goes like this: P "All real numbers have properties X" P ".9999| does not have properties X" C ".9999| is = 1 and it is false that .9999| ≠ 1" If this is what you took from SG's argument, then you understand neither mathematics nor logic...
| This message is a reply to: | | | Message 87 by Jon, posted 01-23-2010 7:27 PM | | Jon has replied |
| Replies to this message: | | | Message 112 by Jon, posted 01-24-2010 4:05 PM | | cavediver has not replied |
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cavediver
Member (Idle past 3670 days) Posts: 4129 From: UK Joined: 06-16-2005
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Message 116 of 237 (544194)
01-24-2010 4:57 PM
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Reply to: Message 110 by Jon
01-24-2010 3:53 PM
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Re: Real Numbers and Real Ity1
So, does the 'real' in 'real numbers' have any relation to the 'real' in 'reality'? Perhaps - we don't know. Next question?
| This message is a reply to: | | | Message 110 by Jon, posted 01-24-2010 3:53 PM | | Jon has not replied |
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cavediver
Member (Idle past 3670 days) Posts: 4129 From: UK Joined: 06-16-2005
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Message 137 of 237 (544247)
01-25-2010 4:21 AM
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Reply to: Message 127 by Rrhain
01-24-2010 7:59 PM
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I guess it's commendable, Rrhain, in some sort of twisted way, but you are so wrong in your beliefs here. All evidence is on my side, and NONE on yours. You have failed already. You of all people should realise that you CANNOT teach a pig to sing... Edited by cavediver, : No reason given.
| This message is a reply to: | | | Message 127 by Rrhain, posted 01-24-2010 7:59 PM | | Rrhain has not replied |
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cavediver
Member (Idle past 3670 days) Posts: 4129 From: UK Joined: 06-16-2005
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Message 145 of 237 (544297)
01-25-2010 10:45 AM
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Reply to: Message 143 by RAZD
01-25-2010 7:33 AM
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Re: ~
In the process it uses another version of 0.999~ and the problem is that if one is not 1 then the other isn't either and it remains half way between. Yes, and neither are assumed to be one. However, they are reasoned to be the same as each other, by virtue of the continued long division. In the same way that you reason that your .999~ multiplied by 2 and with 1 subtracted is also the same, depsite the fact that it would not be true for a terminating decimal .9999.....9
| This message is a reply to: | | | Message 143 by RAZD, posted 01-25-2010 7:33 AM | | RAZD has replied |
| Replies to this message: | | | Message 157 by RAZD, posted 01-25-2010 6:29 PM | | cavediver has not replied |
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cavediver
Member (Idle past 3670 days) Posts: 4129 From: UK Joined: 06-16-2005
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Message 148 of 237 (544313)
01-25-2010 11:52 AM
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Reply to: Message 146 by Jazzns
01-25-2010 11:40 AM
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Re: minor correction
IIRC, pi and e are not irrational, they are transcendental. They are both  What they are not is algebraic.
| This message is a reply to: | | | Message 146 by Jazzns, posted 01-25-2010 11:40 AM | | Jazzns has not replied |
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cavediver
Member (Idle past 3670 days) Posts: 4129 From: UK Joined: 06-16-2005
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You won a math debate... Huh? Sorry, you lost me. But it does remind me of when we had a crowd of 5000, all politely arguing separate points of view. Ah, the joys of mass debating... Now, what were you talking about?
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cavediver
Member (Idle past 3670 days) Posts: 4129 From: UK Joined: 06-16-2005
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did you not read it out loud? Yes, but you obviously didn't read my reply 
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cavediver
Member (Idle past 3670 days) Posts: 4129 From: UK Joined: 06-16-2005
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Message 226 of 237 (545659)
02-04-2010 6:32 PM
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Reply to: Message 225 by lyx2no
02-04-2010 4:10 PM
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Re: A≠B
For the purpose of this thread, why would we care what any average speaker would infer? Quite. Why do the most idiotic of discussions always seem to dominate otherwise sensible threads???
| This message is a reply to: | | | Message 225 by lyx2no, posted 02-04-2010 4:10 PM | | lyx2no has seen this message but not replied |
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