+- Southperry.net (https://www.southperry.net)
+-- Forum: Social (https://www.southperry.net/forumdisplay.php?fid=14)
+--- Forum: Shenanigans (https://www.southperry.net/forumdisplay.php?fid=51)
+--- Thread: 0.9999999 = 1 (/showthread.php?tid=5443)
Pages:
1
2
0.9999999 = 1 - Myles - 2008-11-19
![[Image: c53b723c8dfdc96eb7c8f21a4f481b2c.png]](http://upload.wikimedia.org/math/c/5/3/c53b723c8dfdc96eb7c8f21a4f481b2c.png)
Could be represented as:
1/3 = 0.333333
Therefore 0.66666 = 2/3
0.999999 = 3/3 = 1
wat
0.9999999 = 1 - Kevo - 2008-11-19
Myles Wrote:
Could be represented as:
1/3 = 0.333333
Therefore 0.66666 = 2/3
0.999999 = 3/3 = 1
wat
10x - x doesn't equal 9.
0.9999999 = 1 - psychopat - 2008-11-19
10x - x is 9x, just like 9.999... - 0.999... is 9.
That proof is valid and holds up.
http://en.wikipedia.org/wiki/Proof_that_0.999..._equals_1
0.9999999 = 1 - Kersmack - 2008-11-19
psychopat Wrote:10x - x is 9x, just like 9.999... - 0.999... is 9.
That proof is valid and holds up.
http://en.wikipedia.org/wiki/Proof_that_0.999..._equals_1
yes, because we all know wikipedia is never wrong
0.9999999 = 1 - Roxas - 2008-11-19
Kersmack Wrote:yes, because we all know wikipedia is never wrong
[SIZE="2"][COLOR="RoyalBlue"]It's rarely wrong. You act like it's always wrong and completely unreliable.
By the way, it's true.[/COLOR][/SIZE]
0.9999999 = 1 - Kersmack - 2008-11-19
Roxas Wrote:[SIZE="2"][COLOR="RoyalBlue"]It's rarely wrong. You act like it's always wrong and completely unreliable.
By the way, it's true.[/COLOR][/SIZE]
Where exactly did I say that it's always wrong? My point is people nowadays just use wikipedia as the end-all for any arguments like its undeniable proof.
By the way, I'm familiar with this problem and know that it's true. It just really bugs me when people use wikipedia as their sole argument
0.9999999 = 1 - Atruya - 2008-11-19
1/3 =/= 0.333333
2/3 =/= 0.666666
Therefor: 0.999999 =/= 1/3 + 2/3 so 0.999999 =/= 1.
0.9999999 = 1 - banditcom - 2008-11-19
The title of the thread is wrong.
0.9999999 does not equal 1
0.9999999... does equal 1
And this part is wrong too:
Quote:1/3 = 0.333333
Therefore 0.66666 = 2/3
0.999999 = 3/3 = 1
You need ... to indicate repeating. Those aren't repeating.
The proof is kind of basic (easy to look at). The only reason that proof works is because it is true. There is a real way to prove it other than that simple way as well as the common sense of "find a difference between 0.99999... and 1, there is none", but I don't know that proof off-hand nor do I feel like looking for it. xD
0.9999999 = 1 - Myles - 2008-11-19
banditcom Wrote:The title of the thread is wrong.
0.9999999 does not equal 1
0.9999999... does equal 1
And this part is wrong too:
You need ... to indicate repeating. Those aren't repeating.
The proof is kind of basic but there is a real way to prove it. The only reason that proof works is because it is true.
I know it's recurring, but I couldn't find the recurring sign on the internet ;(
People knew what I meant tho
0.9999999 = 1 - butterfλi - 2008-11-19
banditcom Wrote:You need "[SIZE="7"]...[/SIZE]" to indicate repeating. Those aren't repeating.
Myles Wrote:I couldn't find the recurring sign on the internet ;(
10x - x = (10 - 1)x = 9x
if x = 0.99..., then 9x = (9)(0.99...) != 9
This whole thing revolves around fiddling with invalid operations.
a = b
a^2 = a*b
a^2-b^2 = a*b-b^2
(a+b)(a-b) = b(a-b)
(a+b) = b
a+a = a
2a = a
2 = 1
It's like dividing by 0 and then "proving" that 1 = 2.
0.9999999 = 1 - Alloy - 2008-11-19
10x - x = 9.9999999... - 0.9999999...
THAT is the wrong part. There's a small thing in maths called... infinitesimals.
The MOST small number, consisting in an infinitely small number, thus indefined.
Basically, 0.9999999... is 1 minus an infinitesimal. After multiplying by ten, it goes to...
10(-10 infinitesimals) - 1(+1 infinitesimal)
And taking those out, you get...
9(-9 infinitesimals)
ACTUALLY, by proximity, you get it closer to 8.99999999..., instead of 9.
0.9999999 = 1 - Magus - 2008-11-19
This is why I fucking hate numbers.
There are too many of them.
0.9999999 = 1 - MissAsh - 2008-11-19
Magus Wrote:This is why I pineappleing hate numbers.
There are too many of them.
There is only ten but they get around more than Paris Hilton. ;(
I did 2 programming classes and advanced math in college and flunked them all at least once. NUMBERS ARE EVIL!
0.9999999 = 1 - Alloy - 2008-11-19
MissAsh Wrote:There is only ten but they get around more than Paris Hilton. ;(
I did 2 programming classes and advanced math in college and flunked them all at least once. NUMBERS ARE EVIL!
Specially the small ones... YOU CAN'T SEE THOSE COMING!!!!
0.9999999 = 1 - Kevo - 2008-11-19
The thing I don't get is...
1.000000... = 0.99999999... ?
The numbers are clearly different so how can they be the same. They are as close to each other as can be, but still it's different. Every digit of those two numbers are not the same. The first digit 1 is not equal to 0, and all those 0's don't equal to those 9's.... *confused*
0.9999999 = 1 - Hazzy - 2008-11-19
There's no number between .99... and 1, thus they are the same. D;
0.9999999 = 1 - Alloy - 2008-11-19
Kevo Wrote:The thing I don't get is...
1.000000... = 0.99999999... ?
The numbers are clearly different so how can they be the same. They are as close to each other as can be, but still it's different. Every digit of those two numbers are not the same. The first digit 1 is not equal to 0, and all those 0's don't equal to those 9's.... *confused*
Read my last post... I made it clear, I think.
0.9999999 = 1 - Dusk - 2008-11-19
Kevo Wrote:The thing I don't get is...
1.000000... = 0.99999999... ?
The numbers are clearly different so how can they be the same. They are as close to each other as can be, but still it's different. Every digit of those two numbers are not the same. The first digit 1 is not equal to 0, and all those 0's don't equal to those 9's.... *confused*
It's basically the same thing as Zeno's Paradoxes. No, 0.99999... never reaches 1 if you think of it finitely, but because it keeps going infinitely, the two numbers become the same.
Doesn't matter that the digits are different. 999 is one less than 1,000. 9,999 is one less than 10,000. The paradox results from a weakness in the decimal system that only calculus can eliminate.
0.9999999 = 1 - Kevo - 2008-11-19
Okay, okay I've read all the posts and there's a lot of Maths concepts like infinitesimals and flaws in the decimal system that are kind of confusing. If possible, can somebody explain this using easy-to-understand words? I am in a 1st year Calculus class, with a decent mark, but even so I'm not sure I am understanding what's going on here...
0.9999999 = 1 - Alloy - 2008-11-19
ok...
An infinitesimal can be defined as:
0.000000...
BUT imagine it has a 1 in the end (after infinity zeros), to put it simple. That'd be the smallest number EVER. So small that can't be defined.
0.999999... Would be 1 minus that number, as you can figure out. If you follow the calculus at the first post, it uses an aproximation when multiplying by ten, and takes off those 9 extra infinitesimals, when it shouldn't.
In my post, you see what happens with them, after adding them in. Granted, the result is practically the same, but not exactly.