0.999~ = 1. Prove me wrong.
Author  Topic: 0.999~ = 1. Prove me wrong. 

Apprentice
Member # 4919

written Friday, September 10 2004 11:33
Profile
Homepage
x=.9~ 10x=9.9~ 9x=10xx 9.9~.9~=9. 9=9x Posts: 18  Registered: Sunday, August 29 2004 07:00 
...b10010b...
Member # 869

written Friday, September 10 2004 11:43
Profile
Homepage
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 
Bob's Big Date
Member # 3151

written Friday, September 10 2004 12:35
Profile
Homepage
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 
Master
Member # 4614

written Friday, September 10 2004 14:25
Profile
Homepage
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 
Bob's Big Date
Member # 3151

written Friday, September 10 2004 14:26
Profile
Homepage
Not without invoking fuzzy math.  The biggest, the baddest, and the fattest. Posts: 2367  Registered: Friday, June 27 2003 07:00 
Off With Their Heads
Member # 4045

written Friday, September 10 2004 16:56
Profile
Homepage
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 
...b10010b...
Member # 869

written Friday, September 10 2004 17:14
Profile
Homepage
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 
Agent
Member # 2820

written Friday, September 10 2004 17:16
Profile
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 
One Thousand Slimy Things
Member # 66

written Friday, September 10 2004 18:23
Profile
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 
Lifecrafter
Member # 59

written Friday, September 10 2004 19:38
Profile
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 
Agent
Member # 2820

written Saturday, September 11 2004 06:55
Profile
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 
Master
Member # 4614

written Saturday, September 11 2004 10:46
Profile
Homepage
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 
Apprentice
Member # 4919

written Saturday, September 11 2004 16:01
Profile
Homepage
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 
Agent
Member # 2820

written Saturday, September 11 2004 18:54
Profile
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 
Post Navel Trauma ^_^
Member # 67

written Sunday, September 12 2004 01:18
Profile
Homepage
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 
Lifecrafter
Member # 1768

written Sunday, September 12 2004 11:03
Profile
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 