0.999 exactly equal to 1?

What are you talking about knucklehead? That doesn't abuse math at all, it's simply 0/2, which is a nonsense equation, common knowledge.

Back to the problem of 1 and .99... They are "the same only different" As my symbolic logic professor used to say. For purpses of basic arithmetic they can be considered identical and no it is not merely a matter of rounding. If .99... ever comes up in say banking or architecture or some such it can and always is considered to be indentical to 1. In higher maths though where a simple arithmetical result or "answer" is not the point the two must be treated as being distinct.

 

5/9=.555 repeating
7/9=.777 repeating
9/9=.999 repeating and 9/9 is obviously 1

 

The term "cold" is relative.

Heat on the other hand, is the measure of molecular motion.


Twice as cold, as in half the difference to absolute zero? -136 C...?
----------

The misleading bit of that math problem is that 9.999 is a representation of (10X) .999... And when we subtract .999 from 9.999, we don't get 9, we ACTUALLY get 8.999 because it is now (9X) .999...

 

Oops, I'd read the thing about cold wrong. It's still not a problem for maths though. The designation -273.15 °C as absolute zero isn't a true negative number. It is merely 273.15 degrees less than the temperature at which salt water freezes in the celcius scale, degrees are still degrees, they don't become negative degrees when the temperture drops below zero. The real problem is that the celcius scale is less than adequate and presents aparent though not actual problems here. On the Kelvin scale for example absolute zero is 0 degrees and there is no such thing as "below zero".

 

from looking around it would appear that 1 = 0.99999!

its just like 1/3 = 0.3333 recurring, 1 divided by three creates a recurring number.

the decimal number is only a representation of 1/3, 1 split by 3 equally. the recurring decimal points to 1 split by three. looking at things decimally and out of context proves to be confusing.

in the same way that 1 = 0.9999....

the recurring decimal infers that it is another way of writing 1

on one hand: what still troubles me is the use of the = sign, i'd opt for the approximate sign, maybe when we use recurring decimals we should use the approximate sign to make things happier??

on the other hand: i realise that a recurring number simply points to a number split equally that creates a recurring decimal number. when you reference this recurring number with one with no recurring decimals it looks incorrect.


its a crazy world.

 

thinking again and reiterating

0.999 recurring is simply the decimal equvalent of 1, even though it "doesn't look right"

the science forum i posted on came up with different perspectives some that i didn't understand!! the simplest answer came with the observation that the decimal system didn't really represent recurring numbers. in as many words!

i suppose when we look at recurring numbers we have to understand that though the number trails off into the distance it is the only way we can represent the number decimally.

one third of an apple pie is easily understood
0.3333... of a pie suggests that the number approaches one third of an apple pie
but never reaches the magical one third

hence my origianal line of thought that something must be wrong with the numbers we are using. i stick to my original thought that if you want to use the number 0.333.. you have to tailor what you are using it for. if you had a spaceship flying through space at a quick rate of knots, you would have to use many decimal places behind the 0.3 to get some accuracy behind the calculation you were performing. it wouldn't surprise me if spacecraft would be using computers that used many decimal places in their programming.

eg v = a * t
a = 0.3m/s2
t = 0.3s

v = 0.3 * 0.3 = 0.09m/s (1 decimal place)

v=0.3333333*0.3333333 = 0.11111088 (7 decimal places)

0.11111088 - 0.09 = 0.02111 difference

in space travel this could make the difference between a success and a failure i'd say, of course you'd have then have to realise that if many calculations were being done per second then the error of the final answer would also contribute to how accurate any answer was.

fin

 

Correct me if I'm wrong... but the only reason why 1 seems to equal .9 reapeating is because you have to use some rounding of some sort to do it. If there is an infinit number of .999's then you can't calculate infinity like that right? Because you'd have to stop at some 9 somewhere.

Also if there is a small difference between the numbers no matter how insanly small there is a difference. So 1 doesn't equal .9 repeating because well there is that small difference no matter how impractical it may be.

 

well that was what i started thinking

i was thinking that the 0.999... wasn't equal to 1

the thing is this - our decimal system is a strange beast when it comes to recurring numbers
if you split a pie into three equal pieces you'd think fine, the pie is split into thirds
ie 1/3

if i divided the number 1 by 3 i'd get this number 0.33333....... recurring
decimally if i did this on the calculator for example then tried to add the numbers up by adding the decimal thirds up i wouldn't get 1 i'd get something less than 1, you'd get 0.9999999... recurring

what you have to realise as i did, that the number 0.999.... is the only way we can represent the number 1/3

it is not a case of the number 0.9999999 ending somewhere or for that matter getting closer and closer to the number 1, it is because the number 1/3 can only be represented decimally in the form 0.3333.....

i had my earlier suspicions because there was a problem with what should be represented and what was being represented, and i started to take the route that not all was well with the way the number was being represented.

my own feeling now is that the way we are using the recurring decimal in the original equation is a problem. because there is no way 0.9 = 1
0.999.. recurring = 1 though

 

look dude, it's simple.... they might be so close you can't measure the difference, but the simple fact is you don't push the same buttons to type it so they're not the same number...

 

What are you talking about? It equals one. It's just that there is the rounding off error again. Take that 1/3 turn it into a decimal by dividing 1 by 3 and you get .3 repeating. Times it back by 3 (to nul out the division) and it turns into one again. But if you just insert .33333 etc into a calcuator and times that by 3 it doesn't work out because you only enter in so many 3's and it doesn't know you want .3 repeating instead.

 

10x = 9.99999...
9x = 8.99999...
8x = 7.99999...
7x = 6.99999...
6x = 5.99999...
5x = 4.99999...
4x = 3.99999...
3x = 2.99999...
2x = 1.99999...
1x = .99999...

10X - X = 8.99999...

 

to make things clearer
0.9 recurring is a number that can't be shown "properly"

1 divided by three is 0.3 recurring that is the threes go on forever, we don't have a calculator big enough to ever show this! write out the calculation BY HAND and you'll know what i'm going on about.

the number 0.3 recurring is the DECIMAL representatation of 1/3
the number 0.9 recurring is the DECIMAL representation of 1

the calculation 1 / 3 gives a recurring number what ever the calculator makes of it is whatever the calculator has programmed into it.

n = 0.9 recurring
we know that the ONLY number n can be is 1
hence substituting 1 for n we get
n = 0.9.... recurring
1 = 0.9.......
10 *1 = 9.9....
10 * 1 - 1 = 9.9.... - 0.9.....
9 * 1 = 9
1 = 9/9
1 = 1
1 = 0.9 recurring as 0.9 recurring is also 1
n=0.9.....

removed part in edit here

n is 1 in the very beginning it just isn't shown yet.

 

What are you talking about? Only a fraction can have a decimal representation. there is NO decimal representaion of 1. 1 is just 1. 1/3 has a decimal representation because it's FRACTION meaning that it is LESS than 1. 1 is not less than 1. 1 = 1 the end.

 

i'm not wasting more time on this

the number 1/3 (or one divided by three) gives 0.3 recurring this is the decimal representation of the fraction, no more, no less, 0.3 recurring is the only way we can express one third,1/3, one divided by three, or any other combinations like 2/6, 3/9 etc etc. the recurring threes piling up behind the decimal point are the only way we can represent 1/3

1/ what number gives 0.9 recurring?

1/x = 0.9 recurring?

x= 1.0000000 recurring (in lower calculations you see ones behind the decimal point)

0.9 recurring is just the decimal way of expressing 1
in the same way 0.3 recurring expresses 1/3

end of story

we are intially programmed to accept decimal representations as gospel. when recurring decimals come along it frys our brains when we have to come to terms with the fact that in these case they are just a decimal representation i suppose. any way.. it fried my brains when i first saw it!! if you can't except the algebraic proof (as i couldn't when i first saw it - i started making all sorts of justifications as to why n couldn't be equal to 1! it just didn't make "sense"!!! as to any concept - first there is rejection, then if you start thinking about it and you start thinking on the merits of all ideas presented then you start to appreciate the merits of the new idea when they can be justified and proven, sometimes the answer doesn't fit our view of the world . my earlier posts reflect my inital thinking, as you can see i wasn't happy with it!! how on earth does 1 = 0.9 recurring thats crazy talk!!! as usual i did some research on this and start thinking independently to get my head around it and realised that another way to understand the mathematical truth without algebra (which appeared confusing) was to understand recurring numbers are the way the decimal system represents these starnge numbers - it wasn't something i had come across before. at the moment you are in the rejection stage - good it means you're thinking, just a few more steps until the eureka moment and you realise 1 = 0.9 recurring
good luck!!!

 

ok

no it isnt - its 9.99

10x - 1x = 8.99 = 9.99 - 1x
Actually this whole thing is rubbish

ok so tell me how any of you came to this conclusion
x=.999 10x=9.999 ??????????????????????????

The fact stated was that x=.999
if it had meant x=.999 recurring it wold have been written x=.999r

I think there is one proof that gets somewhere near showing the proof but
even that had to end by saying well they normally round things up.
In actual fact I know someone who wrote as a mathematical thesis
a proof that 0 = 1 (or something that absurd)
to prove that apparently took about 30 pages of A4 sized paper and very small handwriting but it was done and approved by the professors of mathematics. so I doubt that there is proof that .999 = 1 unless you are prepared to make a fantastic attempt at a huge mathematical eqution that involves really complex stuff

 

Dude, It doesn't matter if it's .0 repeating. You can add a million zeros after the decimal point and it'd still equals the same whole number as before. 1.000 = 1 and 2.000 = 2. It doesn't matter when it comes to 0. .0 doesn't make the number less than whole. That's what a decimal is for. To indicate something less than 1. So adding zero after the decimal point is compleatly unessisary. Therfore 1/1.0repeating = 1. Not .999 How do you even get 9 when you divide a number by itself? That doesn't make any sence. 1/1 = 1. Again there is no decimal representation of 1 because 1 is a WHOLE number. Decimal = LESS than a whole number (less than 1).

 

blank mind .........................................
terminal mathematics .....................................
does not compute...............................
machine going down ............................

 

I HAVE THE PROOF -------
It is .999 reccuring
and the fact that you cannot subtract .9 from 9.9999r
without getting the answer of 9.999 - .9 = 9.999

so x= .999
y = 9.999
y-x=9.999

Code:

[font=arial][size=-1][b]Proof:[/b]
    
    lim(m --> ∞) sum(n = 1)^m (9)/(10^n) = 1 
       0.9999... = 1
     
       Thus     x = 0.9999...  
              10x = 9.9999... 
          10x - x = 9.9999... - 0.9999... 
               9x = 9 
                x = 1.[/size][/font]

yes folks the original poster was right .999 does = 1

The final proof is this

take the fractions
1/3 and 2/3

1/3 = .3333333
2/3 = .666666666
3/3 = .99999

unfortunately I am not the genius - this guy is :
http://www.blizzard.com/press/040401.shtml

If you want proof from a genuine mathematician - here it is
http://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html

 

thank you, thank you

 

No problem I just have to change into my cape and mask and go save Lois Lane from a Meteorite that s hurtling to earth now.
DAMMIT we all must be retards if we didnt work that out as a kid
Damn how could I not have seen this before?

1/3 = .333
2/3 = .666
3/3 = .999

The proof
also

[size=-1]x = 0.9999...
10x = 9.9999...
10x - x =9.9999...
9x = 9
x = 1.






and one further mindfuck - go to google calc
type into google .99999999999999 + 0
the answer will be 1
however I discovered a flaw because if you type
.9999999999999 + [/size][size=-1].9999999999999 the answer says 2 and thats gotta be wrong

I found this at a math forum
http://mathforum.org/dr.math/faq/faq.0.9999.html
[/size]

Another informal argument is to notice that all periodic numbers such as 0.9999... = 9/9 = 1 are equal to the digits in the period divided by as many nines as there are in the period. Applying the same argument to 0.46464646... gives us = 46/99.