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: November 21, 2024, 4:44 am
Atheist Forums › Science › Mathematics v
Question for finitists -- 0.999... = 1?

Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Thread Modes
Question for finitists -- 0.999... = 1?
Jehanne Away
Senior Member
****
Religious Views: n/a
Posts: 7259
Threads: 506
Joined: December 12, 2015
Reputation: 22
#1
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!



Find
Reply
Peebothuhlu Offline
Senior Member
****
Religious Views: N/A
Posts: 2755
Threads: 8
Joined: November 28, 2014
Reputation: 22
#2
RE: Question for finitists -- 0.999... = 1?
June 19, 2021 at 4:49 am
At work.

Oh...... 'Maths'....

*Brain fritz*
Find
Reply
BrianSoddingBoru4 Offline
Power-Drunk Administrator
*******
Religious Views: Headology
Posts: 46076
Threads: 538
Joined: July 24, 2013
Reputation: 109
#3
RE: Question for finitists -- 0.999... = 1?
June 19, 2021 at 5:02 am
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
Find
Reply
Sal Offline
The fool
****
Religious Views: agnostic atheist apostate
Posts: 2692
Threads: 11
Joined: May 13, 2013
Reputation: 17
#4
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
Find
Reply
UniversesBoss Offline
Banned
Religious Views: Fatalist
Posts: 30
Threads: 5
Joined: November 26, 2022
Reputation: 0
#5
RE: Question for finitists -- 0.999... = 1?
November 26, 2022 at 1:34 am
0.999=0.999
1=1
Find
Reply
LinuxGal Offline
Member
***
Religious Views: none
Posts: 1988
Threads: 93
Joined: October 23, 2022
Reputation: 8
#6
RE: Question for finitists -- 0.999... = 1?
November 26, 2022 at 12:21 pm
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
Find
Reply
polymath257 Offline
Member
***
Religious Views: Atheist
Posts: 2412
Threads: 5
Joined: January 3, 2018
Reputation: 22
#7
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:

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

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.
Find
Reply
LinuxGal Offline
Member
***
Religious Views: none
Posts: 1988
Threads: 93
Joined: October 23, 2022
Reputation: 8
#8
RE: Question for finitists -- 0.999... = 1?
November 26, 2022 at 5:54 pm
(November 26, 2022 at 5:17 pm)polymath257 Wrote: 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.

Not so, since x = 0.999... has an upper bound as the decimal expansion continues without limit, but x = 1+2+4... diverges.
Find
Reply
HappySkeptic Offline
Member
***
Religious Views: What god?
Posts: 1659
Threads: 5
Joined: September 26, 2018
Reputation: 12
#9
RE: Question for finitists -- 0.999... = 1?
November 26, 2022 at 6:04 pm
(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.
Find
Reply
rocinantexyz Offline
Newbie
*
Religious Views: atheist
Posts: 16
Threads: 1
Joined: November 22, 2022
Reputation: 0
#10
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 )
Warning: the following post contains a contiguous slice that is a PART of a larger post:
(November 26, 2022 at 6:04 pm)HappySkeptic Wrote: I'm not sure if your proof is valid...
It was valid in discrete math class when I was in University.
Find
Reply


Atheist Forums › Science › Mathematics v
Question for finitists -- 0.999... = 1?

Possibly Related Threads...
Thread Author Replies Views Last Post
  Mathematicians who are finitists. Jehanne 99 15664 July 11, 2019 at 1:53 pm
Last Post: A Toy Windmill
  Maths proves 1=0.999.. thus ends in self contradiction shakuntala 11 6419 December 21, 2014 at 3:57 pm
Last Post: Thumpalumpacus
  If 0.999(etc) = 1, does 1 - 0.999 go to zero? Euler 26 10026 April 30, 2013 at 12:17 pm
Last Post: Mister Agenda
  [split] 0.999... equals 1 Rhizomorph13 330 113992 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 11546 March 6, 2012 at 2:12 pm
Last Post: Child of Stardust



Users browsing this thread: 2 Guest(s)