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: April 18, 2024, 12:37 am
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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
‘But it does me no injury for my neighbour to say there are twenty gods or no gods. It neither picks my pocket nor breaks my leg.’ - Thomas Jefferson
 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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