Register | Sign In


Understanding through Discussion


EvC Forum active members: 65 (9164 total)
5 online now:
Newest Member: ChatGPT
Post Volume: Total: 916,435 Year: 3,692/9,624 Month: 563/974 Week: 176/276 Day: 16/34 Hour: 2/7


Thread  Details

Email This Thread
Newer Topic | Older Topic
  
Author Topic:   0.99999~ = 1 ?
Briterican
Member (Idle past 3970 days)
Posts: 340
Joined: 05-29-2008


Message 3 of 237 (543080)
01-15-2010 8:49 AM
Reply to: Message 2 by cavediver
01-15-2010 8:42 AM


Hmm, equal?
cavediver writes:
Huntard writes:
It is my understanding that 0.9999~ does indeed equal 1.
Yes, indeed it does... unless you happen to be a constructivist, that is!
Shouldn't there be some sort of conditional involved or something? I don't see how it could be considered accurate to say that 0.99999~ is precisely equivalent to 1.
I appreciate that, for all intents and purposes, they are equivalent. But mathematically they simply are not, right?
Maybe I'm missing something.

This message is a reply to:
 Message 2 by cavediver, posted 01-15-2010 8:42 AM cavediver has not replied

Replies to this message:
 Message 5 by Huntard, posted 01-15-2010 9:04 AM Briterican has seen this message but not replied
 Message 8 by Dr Jack, posted 01-15-2010 10:25 AM Briterican has replied

  
Briterican
Member (Idle past 3970 days)
Posts: 340
Joined: 05-29-2008


Message 9 of 237 (543100)
01-15-2010 11:10 AM
Reply to: Message 8 by Dr Jack
01-15-2010 10:25 AM


Re: Hmm, equal?
Yeah I get it now.
My brain doesn't want to cooperate, but thanks to the specific examples given by you guys, I understand now.
Well... I am 99.99999~% sure that I understand anyway

This message is a reply to:
 Message 8 by Dr Jack, posted 01-15-2010 10:25 AM Dr Jack has seen this message but not replied

Replies to this message:
 Message 12 by RAZD, posted 01-15-2010 5:37 PM Briterican has replied
 Message 13 by PaulK, posted 01-15-2010 5:51 PM Briterican has replied

  
Briterican
Member (Idle past 3970 days)
Posts: 340
Joined: 05-29-2008


Message 14 of 237 (543155)
01-15-2010 6:14 PM
Reply to: Message 12 by RAZD
01-15-2010 5:37 PM


Equivalence for repeating decimals!
Hi RAZD
As always, nice presentation.
RAZD writes:
My personal favorite repeating decimal fraction is 7ths
These sorts of things are fascinating. Even the simple graphic representation you provided using a yellow font to show the repeating pattern is fascinating. (My favourite example of this kind of thing is the Mandlebrot Set, which has nothing to do with 1=0.999~ but is an example of visualised mathematics).
Even wiki has a large page regarding .999999~
I wonder what other sort of mathematics concepts I'm underinformed on hehe.

This message is a reply to:
 Message 12 by RAZD, posted 01-15-2010 5:37 PM RAZD has seen this message but not replied

  
Briterican
Member (Idle past 3970 days)
Posts: 340
Joined: 05-29-2008


Message 15 of 237 (543156)
01-15-2010 6:17 PM
Reply to: Message 13 by PaulK
01-15-2010 5:51 PM


Re: Hmm, equal?
PaulK writes:
That is, two numbers a and b are equal if there is no number, e such that
|a - b| < e
(Which is the same as saying that there is no number between them, if you think about it).
This illuminates the matter even further.
I thank you, and Huntard for the OP as well.

This message is a reply to:
 Message 13 by PaulK, posted 01-15-2010 5:51 PM PaulK has not replied

  
Briterican
Member (Idle past 3970 days)
Posts: 340
Joined: 05-29-2008


Message 51 of 237 (543386)
01-17-2010 5:00 PM
Reply to: Message 49 by Huntard
01-17-2010 4:24 PM


Re: On infinities
Hi Huntard
Wow, infinity ("the abyss") really drove Cantor crazy hehe.
Thanks for the link, I was looking for something to watch tonight (as opposed to watching "The Wire" for the third time).
Thanks for the link.

This message is a reply to:
 Message 49 by Huntard, posted 01-17-2010 4:24 PM Huntard has not replied

  
Briterican
Member (Idle past 3970 days)
Posts: 340
Joined: 05-29-2008


Message 68 of 237 (543471)
01-18-2010 10:57 AM
Reply to: Message 65 by Straggler
01-18-2010 9:32 AM


Re: 0 and Infinitesimally Small - Something and Nothing
straggler writes:
Except that it still seems like 0.999R should be infinitesimally less than 1. Which I suppose it is. If by infinitesimally small we mean tending to 0.
That's how my brain wanted to approach the problem, but several members posted this very useful way of looking at it...
1/3 + 1/3 + 1/3 = 1
1/3 = .333R
.333R + .333R + .333R = .999R
therefore .999R = 1
Precisely and exactly equal.
Edited by Briterican, : No reason given.

This message is a reply to:
 Message 65 by Straggler, posted 01-18-2010 9:32 AM Straggler has replied

Replies to this message:
 Message 69 by Straggler, posted 01-18-2010 1:08 PM Briterican has seen this message but not replied

  
Newer Topic | Older Topic
Jump to:


Copyright 2001-2023 by EvC Forum, All Rights Reserved

™ Version 4.2
Innovative software from Qwixotic © 2024