Is 1 = 0.9999......

Page 45 - Seeking answers? Join the AnandTech community: where nearly half-a-million members share solutions and discuss the latest tech.

mchammer187

Diamond Member
Nov 26, 2000
9,114
0
76
every time i see this thread bumped i get angry

.99... = 1 !

.99.. does not approach 1 it IS 1

1/x approaches zero

1-.99... = 0.00..1 is ridiculous because it assumes an infinite series of 0's terminates when in fact it does not


 

Simoncifer

Junior Member
Dec 16, 2002
9
0
0
Actually, it is yes and no, depending on which field of math you are talking about. If you are talking about Applied Math (for science or engineering), it is yes, 0.99999... = 1 (it is close enough.....). However, if you are talking about Abstract Algebra or Number Theory, then no. The reason is that 0.999999...... is a rational number (by the definite of rational number), and since it is a rational number, there exist 2 INTEGERS, p and q, such that p/q = 0.9999999..... (Don't know what those 2 integers are since I didn't have enough sleep last night, I am very sleepy and tire this morning..... noon..... day).

Since I didn't read all the posts, someone might have mentioned this already, and this becomes a repost. If that's the case, I am sorry about the repost....
 

Jeff7181

Lifer
Aug 21, 2002
18,368
11
81
lets try this...

x=0.9r
y=1
we want to prove that x=y

(10x)/y=(9.9r)/1 correct?
(10x)/y=(9.9r) correct?
10x=(9.9r)y correct?
(10x)/9.9r=y correct?
10x=9.9r correct?
10x/10x = y correct?
10x/10x = 1
y=1

therefore x does not = 1 and y does not equal x
 

dighn

Lifer
Aug 12, 2001
22,820
4
81
Originally posted by: Jeff7181
lets try this...

x=0.9r
y=1
we want to prove that x=y

(10x)/y=(9.9r)/1 correct?
(10x)/y=(9.9r) correct?
10x=(9.9r)y correct?
(10x)/9.9r=y correct?
10x=9.9r correct?
10x/10x = y correct?
10x/10x = 1
y=1

therefore x does not = 1

the onlything you proved there is that 1 = 1

nowhere in that proof implies x != 1
 

Jeff7181

Lifer
Aug 21, 2002
18,368
11
81
You see the error I purposely made... but you don't see it in the origional equation... hmmmm =)
 

dighn

Lifer
Aug 12, 2001
22,820
4
81
Originally posted by: Jeff7181
You see the error I purposely made... but you don't see it in the origional equation... hmmmm =)

err

how aboti drop the x's


9*0.9r = (10-1)*0.9r = 9.9r - 0.9r = 9
9*0.9r = 9
0.9r = 1
 

Jeff7181

Lifer
Aug 21, 2002
18,368
11
81
Originally posted by: Muzzan
Where is the error in the original equation?

Please do tell.

Look at the 2nd line of mine... then look at the origional equation again
 

Muzzan

Member
Apr 15, 2003
169
0
0
I see no mistake in either (except your conclusion). Your second line is simply stating the obvious (that (10 * 0,9r) / 1 =9,9r).

Which part of the original equation do you disagree with?

That 10x - x = 9x?
That 9,999... - 0,999... = 9?
Or that the two are equivalent?
 

Jeff7181

Lifer
Aug 21, 2002
18,368
11
81
0.9999... = 1

Thus x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.

what if I do this...


x=0.9r
10x = 9.9r
10x-x = 9.9r - 0.9r
now to simplify, we ad x to each side of the equation
(10x - x) + x = 9.9r - 0.9r + x
9x = 9 + x


Sorry bout all the edits... I know my typos screw you guys up, lol
 

Muzzan

Member
Apr 15, 2003
169
0
0
Originally posted by: Jeff7181
0.9999... = 1

Thus x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.

what if I do this...


x=0.9r
10x = 9.9r
10x-x = 9.9r - 0.9r
now to simplify, we ad x to each side of the equation
(10x - x) + x = 9.9r - 0.9r + x
9x = 9 + x

I do not wish to be rude, but you really need to work on your arithmetic.

10x - x + x = x(10 - 1 + 1) = x(10) = 10x.
 

Jeff7181

Lifer
Aug 21, 2002
18,368
11
81
Originally posted by: Muzzan
Originally posted by: Jeff7181
0.9999... = 1

Thus x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.

what if I do this...


x=0.9r
10x = 9.9r
10x-x = 9.9r - 0.9r
now to simplify, we ad x to each side of the equation
(10x - x) + x = 9.9r - 0.9r + x
9x = 9 + x

I do not wish to be rude, but you really need to work on your arithmetic.

10x - x + x = 10x.


I know, I'm typing fast and making typos
 

DrPizza

Administrator Elite Member Goat Whisperer
Mar 5, 2001
49,601
167
111
www.slatebrookfarm.com
Originally posted by: Simoncifer
Actually, it is yes and no, depending on which field of math you are talking about. If you are talking about Applied Math (for science or engineering), it is yes, 0.99999... = 1 (it is close enough.....). However, if you are talking about Abstract Algebra or Number Theory, then no. The reason is that 0.999999...... is a rational number (by the definite of rational number), and since it is a rational number, there exist 2 INTEGERS, p and q, such that p/q = 0.9999999..... (Don't know what those 2 integers are since I didn't have enough sleep last night, I am very sleepy and tire this morning..... noon..... day).

Since I didn't read all the posts, someone might have mentioned this already, and this becomes a repost. If that's the case, I am sorry about the repost....

According to Godel's famous proof, it can't be proven that there will never be a contradiction in math.... However, at this point, there have been no contradictions. What you are suggesting is that developments in two different branches of mathematics have yielded a contradiction... hasn't happened.
 

Simoncifer

Junior Member
Dec 16, 2002
9
0
0
I think what he meant was that 9.99999.... - 0.99999..... != 9. Because if you substitute x = 0.99999......., then you get

9.99999........ - 0.99999....... = 10x - x = 9x , not 9
 

Jeff7181

Lifer
Aug 21, 2002
18,368
11
81
I guess I'll stop trying, lol... my typos have me confused now and I forget where I was going with something, lol
 

Simoncifer

Junior Member
Dec 16, 2002
9
0
0
No, I am stating that for all purpose of Applied Math, 0.99999..... = 1. But strictly speaking, like in number theory or abstract algebra, 0.99999.... != 1.
 

Muzzan

Member
Apr 15, 2003
169
0
0
Originally posted by: Jeff7181
I guess I'll stop trying, lol... my typos have me confused now and I forget where I was going with something, lol

Another one bites the dust
 

Jeff7181

Lifer
Aug 21, 2002
18,368
11
81
I'm a logical person, and logic says that only 1=1... but we're dealing with an infinite number here, and maybe the humain brain can't comprehend infinite numbers... at least mine can't anyway, lol.
 

Simoncifer

Junior Member
Dec 16, 2002
9
0
0
Actually, to be the "Devil's Advocate" and confuse people more,

1/9 = 0.111111........

9 * (1/9) = 9 * (0.111111.........)

hehehe, the rest is more fun for you to figure out yourself. (I am surprise no one mention this one, just keep mentioning the one "proof" in the original post).
 

Muzzan

Member
Apr 15, 2003
169
0
0
Simoncifer: oh, it's been mentioned before. But I can't remember where in the ~20 pages or so of discussion
 

Jeff7181

Lifer
Aug 21, 2002
18,368
11
81
They say mathematics is the only universal language... maybe it's not... maybe 1+2 doesn't equal 3... according to this it might be 2.9r, lol... my head hurts =)
 

pipster

Member
Nov 27, 2001
122
0
0
Fun to reflect on, but not as interesting as pondering what 0/0 equals (zero divided by zero):

is it equal to zero?
is it equal to one?
is it equal to infinity?

Perhaps deserving its own poll/thread, i'm sure some unsuspecting lady or gentlemen will open that pandora's box someday...

(excuse the NooBness if this has already been done before...)
 

dighn

Lifer
Aug 12, 2001
22,820
4
81
Originally posted by: pipster
Fun to reflect on, but not as interesting as pondering what 0/0 equals (zero divided by zero):

is it equal to zero?
is it equal to one?
is it equal to infinity?

Perhaps deserving its own poll/thread, i'm sure some unsuspecting lady or gentlemen will open that pandora's box someday...

(excuse the NooBness if this has already been done before...)

could be anything hence the name "indeterminate"
 

Jeff7181

Lifer
Aug 21, 2002
18,368
11
81
0 divided by anything is indeterminate... because you're saying you have nothing to start out with, so you can't divide it into smaller parts, cause you have NOTHING =)
 

DrPizza

Administrator Elite Member Goat Whisperer
Mar 5, 2001
49,601
167
111
www.slatebrookfarm.com
Originally posted by: Simoncifer
No, I am stating that for all purpose of Applied Math, 0.99999..... = 1. But strictly speaking, like in number theory or abstract algebra, 0.99999.... != 1.

Sorry, Simon.... but I graduated magna cum laude with a bachelor's degree in applied mathematics. For applied mathematics, .999 repeating does = 1. But I learned this fact first in an abstract algebra course. .9999repeating = 1 in abstract algebra as well.
 
sale-70-410-exam    | Exam-200-125-pdf    | we-sale-70-410-exam    | hot-sale-70-410-exam    | Latest-exam-700-603-Dumps    | Dumps-98-363-exams-date    | Certs-200-125-date    | Dumps-300-075-exams-date    | hot-sale-book-C8010-726-book    | Hot-Sale-200-310-Exam    | Exam-Description-200-310-dumps?    | hot-sale-book-200-125-book    | Latest-Updated-300-209-Exam    | Dumps-210-260-exams-date    | Download-200-125-Exam-PDF    | Exam-Description-300-101-dumps    | Certs-300-101-date    | Hot-Sale-300-075-Exam    | Latest-exam-200-125-Dumps    | Exam-Description-200-125-dumps    | Latest-Updated-300-075-Exam    | hot-sale-book-210-260-book    | Dumps-200-901-exams-date    | Certs-200-901-date    | Latest-exam-1Z0-062-Dumps    | Hot-Sale-1Z0-062-Exam    | Certs-CSSLP-date    | 100%-Pass-70-383-Exams    | Latest-JN0-360-real-exam-questions    | 100%-Pass-4A0-100-Real-Exam-Questions    | Dumps-300-135-exams-date    | Passed-200-105-Tech-Exams    | Latest-Updated-200-310-Exam    | Download-300-070-Exam-PDF    | Hot-Sale-JN0-360-Exam    | 100%-Pass-JN0-360-Exams    | 100%-Pass-JN0-360-Real-Exam-Questions    | Dumps-JN0-360-exams-date    | Exam-Description-1Z0-876-dumps    | Latest-exam-1Z0-876-Dumps    | Dumps-HPE0-Y53-exams-date    | 2017-Latest-HPE0-Y53-Exam    | 100%-Pass-HPE0-Y53-Real-Exam-Questions    | Pass-4A0-100-Exam    | Latest-4A0-100-Questions    | Dumps-98-365-exams-date    | 2017-Latest-98-365-Exam    | 100%-Pass-VCS-254-Exams    | 2017-Latest-VCS-273-Exam    | Dumps-200-355-exams-date    | 2017-Latest-300-320-Exam    | Pass-300-101-Exam    | 100%-Pass-300-115-Exams    |
http://www.portvapes.co.uk/    | http://www.portvapes.co.uk/    |