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!
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Current time: December 26, 2024, 11:41 pm
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Question for finitists -- 0.999... = 1?
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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
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