0.999~ = 1. Prove me wrong.
| Author | Topic: 0.999~ = 1. Prove me wrong. |
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Apprentice
Member # 4919
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written Friday, September 10 2004 11:33
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x=.9~ 10x=9.9~ 9x=10x-x 9.9~-.9~=9. 9=9x Posts: 18 | Registered: Sunday, August 29 2004 07:00 |
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...b10010b...
Member # 869
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written Friday, September 10 2004 11:43
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Not this conversation again. You're right, of course, since infinitesimals aren't defined in standard mathematics. -------------------- My BoE Page Bandwagons are fun! Roots Hunted! Posts: 9973 | Registered: Saturday, March 30 2002 08:00 |
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Bob's Big Date
Member # 3151
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written Friday, September 10 2004 12:35
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There is no mathematical proof for .x~ - .x~ = 0 for this very reason. I suppose next you are going to propose that we multiply infinity by zero. -------------------- The biggest, the baddest, and the fattest. Posts: 2367 | Registered: Friday, June 27 2003 07:00 |
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Master
Member # 4614
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written Friday, September 10 2004 14:25
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Or that 1=2 (which has actually been proved before mathematically). -------------------- -ben4808 For those who love to spam: CSM Forums RIFQ Posts: 3360 | Registered: Friday, June 25 2004 07:00 |
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Bob's Big Date
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written Friday, September 10 2004 14:26
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Not without invoking fuzzy math. -------------------- The biggest, the baddest, and the fattest. Posts: 2367 | Registered: Friday, June 27 2003 07:00 |
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Off With Their Heads
Member # 4045
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written Friday, September 10 2004 16:56
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It all depends on your axioms. If you assume that 0 = 1, proving that 1 = 2 is trivial. And more accurately, one should say that the limit of .999 repeating is equal to 1, not that .999 repeating is itself equal to 1. -------------------- Arancaytar: Every time you ask people to compare TM and Kel, you endanger the poor, fluffy kittens. Kelandon's Pink and Pretty Page!!: the authorized location for all things by me The Archive of all released BoE scenarios ever Posts: 7968 | Registered: Saturday, February 28 2004 08:00 |
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...b10010b...
Member # 869
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written Friday, September 10 2004 17:14
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Well, repeating decimals are really just a notation for fractions which can't be expressed in base 10. We wouldn't have to consider their limits unless they were actually equations, which I don't think they are. Regarding the "proofs" of 1 = 2, all of them contain a division step which isn't mathematically valid if the divisor is 0 (which it has to be for the "proof" to work). [ Friday, September 10, 2004 17:17: Message edited by: Thuryl ] -------------------- My BoE Page Bandwagons are fun! Roots Hunted! Posts: 9973 | Registered: Saturday, March 30 2002 08:00 |
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Agent
Member # 2820
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written Friday, September 10 2004 17:16
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Or this: 1/3 = .3~ 2/3 = 1/3 + 1/3 = .3~ + .3~ = .6~ 3/3 = 1 = 1/3 + 1/3 + 1/3 = .3~ + .3~ + .3~ = .9~ The base of numbers really does mess things up, doesn't it? In base 3, 10/3 = .1! EDIT: Wait, I can prove you wrong. When dealing with any real number, a base is just a representation of numbers. Since the symmetrical reflexive property would say that x = x, no matter the base. Note that .1~ is 1/9, but I'll use 1/3 because of familiarity. IN BASE 3: 1/10 = (10/10)/10 = 1 / 10 = .1 Definition of division and the converse of the identity property of multiplication 1/10 * 10 = 1/1 = 1 = 1/10 + 1/10 + 1/10 = .1 + .1 + .1 = 1!! [ Friday, September 10, 2004 17:27: Message edited by: Garrison ] -------------------- What do I put here? -Garrison Posts: 1415 | Registered: Thursday, March 27 2003 08:00 |
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One Thousand Slimy Things
Member # 66
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written Friday, September 10 2004 18:23
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12 posts and I hate him already. [ Friday, September 10, 2004 18:24: Message edited by: Wolfiewoobles ] -------------------- Bending, but not in the way you might imagine. Posts: 995 | Registered: Thursday, October 4 2001 07:00 |
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Lifecrafter
Member # 59
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written Friday, September 10 2004 19:38
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quote:.x~ (in the decimal system) is a representation of the rational number x/9. Each rational number has exactly one additive inverse. Posts: 950 | Registered: Thursday, October 4 2001 07:00 |
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Agent
Member # 2820
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written Saturday, September 11 2004 06:55
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quote:It would be rather hard to explain this math problem because I don't believe there is any rational number that can be expressed as (.9~). Also, what kind of name is SpaceOfAdes???? [ Saturday, September 11, 2004 06:57: Message edited by: Garrison ] -------------------- What do I put here? -Garrison Posts: 1415 | Registered: Thursday, March 27 2003 08:00 |
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Master
Member # 4614
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written Saturday, September 11 2004 10:46
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You can look here. Apparently the proof has a flaw, so I guess I was wrong in the first place. It looks pretty convincing, though. -------------------- -ben4808 For those who love to spam: CSM Forums RIFQ Posts: 3360 | Registered: Friday, June 25 2004 07:00 |
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Apprentice
Member # 4919
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written Saturday, September 11 2004 16:01
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quote:SpaceOfAdes = Ace of Spades.. Ace of Spades is my little nickname among my friends, and most places already have someone called "Ace of Spades", so I became SpaceOfAdes. [ Sunday, September 12, 2004 13:11: Message edited by: SpaceOfAdes1134 ] Posts: 18 | Registered: Sunday, August 29 2004 07:00 |
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Agent
Member # 2820
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written Saturday, September 11 2004 18:54
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Hmmm, rhetorical question. That was a nice classical fallacy you posted, Ben. It was simple as long as you replace all the b variables with the letter a. [ Saturday, September 11, 2004 19:01: Message edited by: Garrison ] -------------------- What do I put here? -Garrison Posts: 1415 | Registered: Thursday, March 27 2003 08:00 |
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Post Navel Trauma ^_^
Member # 67
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written Sunday, September 12 2004 01:18
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0.9~ is equal to 1. It's defined as the limit of 9/10 + 9/100 + 9/1000 + ... as the number of terms goes to infinity, and that limit is exactly 1. 0.9~ - 0.9~ is defined, and is zero. 1 - 0.9~ is also zero, exactly. 0.0000...001 doesn't mean anything. -------------------- Barcoorah: I even did it to a big dorset ram. desperance.net - Don't follow this link Posts: 1798 | Registered: Thursday, October 4 2001 07:00 |
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Lifecrafter
Member # 1768
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written Sunday, September 12 2004 11:03
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Cheese! -------------------- "Oh, North Wind, why frighten others? In Nature's family all are brothers. Puff and blow and wheeze and hiss; You can't frighten Shingebiss. Bring your frost and ice and snow; I'm still free to come and go. You can never frighten me, One who never fears is FREE!" -Shingebiss, the mighty duck Posts: 830 | Registered: Tuesday, August 20 2002 07:00 |