Question for finitists -- 0.999... = 1?
June 18, 2021 at 6:37 pm
(This post was last modified: June 18, 2021 at 6:38 pm by Jehanne.)
And, ultra-finitists, too!
Our server costs ~$56 per month to run. Please consider donating or becoming a Patron to help keep the site running. Help us gain new members by following us on Twitter and liking our page on Facebook!
Current time: December 21, 2024, 11:15 pm
Thread Rating:
|
Question for finitists -- 0.999... = 1?
|
At work.
Oh...... 'Maths'.... *Brain fritz* 
I once had a real, professional mathematician corner me at a party and spend 20 minutes explaining to me why the interval from 0 to 1 is not the same as the interval from 1 to 2.
Because of the resultant trauma, I am unable to watch that video. Boru
‘I can’t be having with this.’ - Esmeralda Weatherwax
 RE: Question for finitists -- 0.999... = 1?
June 19, 2021 at 5:45 am
(This post was last modified: June 19, 2021 at 5:46 am by Sal.)
0.000 ... 001 = 0
1 / ∞
"The first principle is that you must not fool yourself — and you are the easiest person to fool." - Richard P. Feynman
0.999=0.999
1=1
Define:
x = 0.999... Multiply both sides by 10 10x = 9.999... Isolate integer part 10x = 9 + 0.999... By definition of x 10x = 9 + x Subtract x from both sides 9x =9 Divide both sides by 9 x = 1  RE: Question for finitists -- 0.999... = 1?
November 26, 2022 at 5:17 pm
(This post was last modified: November 26, 2022 at 5:18 pm by polymath257.)
(November 26, 2022 at 12:21 pm)LinuxGal Wrote: Define: Step 1: Prove the expression .999.... makes sense. Otherwise, you could argue as follows: x=1+2+4+8+16+... 2x=2+4+8+16+32+... Hence, x=1+2x so -x=1 x=-1 In particular, 1+2+4+8+... <0. (November 26, 2022 at 5:17 pm)polymath257 Wrote: Step 1: Prove the expression .999.... makes sense. Not so, since x = 0.999... has an upper bound as the decimal expansion continues without limit, but x = 1+2+4... diverges.  (November 26, 2022 at 5:54 pm)LinuxGal Wrote: Not so, since x = 0.999... has an upper bound as the decimal expansion continues without limit, but x = 1+2+4... diverges. True. In your case, though, you are performing the same trick - it is just that the additional digit you shifted in is an infinitesimal instead of a large value. I'm not sure if your proof is valid, but of course one can get as close to correct as you like. RE: Question for finitists -- 0.999... = 1?
November 26, 2022 at 6:21 pm
(This post was last modified: November 26, 2022 at 6:22 pm by rocinantexyz.
Edit Reason: typos
)
|
|
« Next Oldest | Next Newest »
|
| Possibly Related Threads... | |||||
| Thread | Author | Replies | Views | Last Post | |
| Mathematicians who are finitists. | Jehanne | 99 | 15905 |
July 11, 2019 at 1:53 pm Last Post: A Toy Windmill |
|
| Maths proves 1=0.999.. thus ends in self contradiction | shakuntala | 11 | 6485 |
December 21, 2014 at 3:57 pm Last Post: Thumpalumpacus |
|
| If 0.999(etc) = 1, does 1 - 0.999 go to zero? | Euler | 26 | 10096 |
April 30, 2013 at 12:17 pm Last Post: Mister Agenda |
|
| [split] 0.999... equals 1 | Rhizomorph13 | 330 | 114919 |
February 20, 2013 at 6:47 am Last Post: Categories+Sheaves |
|
| If 0.999 (etc.) = 1, does 1 - 0.999 = 0? | Child of Stardust | 16 | 11622 |
March 6, 2012 at 2:12 pm Last Post: Child of Stardust |
|
Users browsing this thread: 1 Guest(s)
