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Is 1 = 0.9999......

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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


 
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....
 
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
 
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
Click to expand...

the onlything you proved there is that 1 = 1

nowhere in that proof implies x != 1
 
Originally posted by: Jeff7181
You see the error I purposely made... but you don't see it in the origional equation... hmmmm =)
Click to expand...

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
 
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?
 
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
 
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
Click to expand...

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.
 
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
Click to expand...

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

10x - x + x = 10x.
Click to expand...


I know, I'm typing fast and making typos
 
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....
Click to expand...

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.
 
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
 
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.
 
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.
 
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).
 
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 =)
 
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...)
 
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...)
Click to expand...

could be anything hence the name "indeterminate"
 
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 =)
 
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.
Click to expand...

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.
 
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