Forums - General Discussion - 0.9999.... = 1.0

Are you convinced?

Yes
No
not sure

This is a fairly old topic so I'm not sure if all of you have heard about this. I just found out about it and found it interesting.

The claim is that 0.9999.....(infinite 9s) is equal to 1.

Here are some proofs

-

x = 0.9999… given
10x = 9.9999…. multiply by 10
9x = 9 subtract x
x = 1 divide by 9
0.999... = 1 substitution

What's the difference between 1 and 0.9999....? Their difference is 0.0000....The zeroes will stretch out infinitely and we will never reach 1. Therefore, 0.00000...can be simplified to 0.

If the difference between any two numbers is 0, then they are of the same value.

On the number line, there is no real number between 0.99999..... and 1. If there is no real number between any two numbers, then those two numbers are of the same value. There is no number higher than 0.9999... and lower than 1, therefore they are of the same value.

1= 7/7 
1= 5/7 + 2/7 
1= 0.714285714285.... + 0.285714285714......
1= 0.999999999999

Sum of an infinite convergent geometric series


0.999ldots = 9left(tfrac{1}{10}right) + 9left({tfrac{1}{10}}right)^2 + 9left({tfrac{1}{10}}right)^3 + cdots = frac{9left({tfrac{1}{10}}right)}{1-{tfrac{1}{10}}} = 1.,

and many more



Around the Network
really......slow......news......day.........

But the difference between 0.9999... and 1 is .1 not 0. The 0.99999... seems like a perpetual state of waiting for that .1 but it never coming, like third parties for Nintendo.

SIG2 (2) Week 1

I earned "Proof of Omega", killed the FF7 Weapons, attained "Big Boss" in the "Patriots", found and killed the Red Chocobo in FFXII, platinumed Killzone 2 and LBP. What you got bitch!? Huh?

The problem comes when you operate on an infinite scale. There's no way you can reach infinite. Infinite + 1 = Infinite. Going by that logic, yeah, the diference between 1 to 0'9999...Ěn Infinite is 0000000.... Ěn Infinite + 1. And Infinite + 1 = infinite. So there's no difference between 1 and 0'99999....

AbbathTheGrim said:
But the difference between 0.9999... and 1 is .1 not 0. The 0.99999... seems like a perpetual state of waiting for that .1 but it never coming, like third parties for Nintendo.


wouldn't it be 0.0001?

Sorry Jay Im not good enough in math to tell you.  I do know that you can make a plausible equation for 1+1=3

The quote "once you make something impossible possible.  Anything can be possible."  Or something like that although I'm pretty sure I got the quote wrong.



An Unbiased Review                Breaking News!  Naughty Dog Third Party!          

Around the Network
Pretty cool. I never realized. :-O

0.999....

9 is a periodic number.

9/9 (The other 9 is the number of figures of the periodic part)

9/9 = 1

AbbathTheGrim said:
But the difference between 0.9999... and 1 is .1 not 0. The 0.99999... seems like a perpetual state of waiting for that .1 but it never coming, like third parties for Nintendo.

Shit, that made me laugh.



JayWood2010 said:
AbbathTheGrim said:
But the difference between 0.9999... and 1 is .1 not 0. The 0.99999... seems like a perpetual state of waiting for that .1 but it never coming, like third parties for Nintendo.


wouldn't it be 0.0001?

Sorry Jay Im not good enough in math to tell you.  I do know that you can make a plausible equation for 1+1=3

The quote ends "once you make something impossible possible.  Anything can be possible."  Or something like that although I'm pretty sure I got the quote wrong.

Sir, if you are bad at math I am atrocious.  It would depend on where the last .9 was at, I think.



SIG2 (2) Week 1

I earned "Proof of Omega", killed the FF7 Weapons, attained "Big Boss" in the "Patriots", found and killed the Red Chocobo in FFXII, platinumed Killzone 2 and LBP. What you got bitch!? Huh?

AbbathTheGrim said:
But the difference between 0.9999... and 1 is .1 not 0. 


Nope, it's zero. 

1 - 0.9 = 0.1

1 - 0.99 = 0.01

1 - 0.9999 = 0.0001

But when you have infinite nines, you also have infinite zeros and never reach the 1. 

  1.0000000000000000........
- 0.9999999999999999.........
=0.0000000000000000........

At no point will you ever reach ....0001.



Around the Network
JayWood2010 said:

  I do know that you can make a plausible equation for 1+1=3

For reasonably large values of 1, this equatiion is true