0.999r = 1

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DeletedUser

x = 0.999 r
10x = 9.999 r
10x-x = 9x
9x = 9
x=9

OR another explanation


9/9 = 1

1/9 = 0.111r
9x1/9 = 0.999r
0.999 = 1
 

DeletedUser14280

Convert the following fractions to decimal equivalents (use underline to indicate recurring digits).
1/9 = 0.1
2/9 =
4/9 =
5/9 =
8/9 =
9/9 =
 

nashy19

Nashy (as himself)
Basically everything is this section: http://en.wikipedia.org/wiki/0.999...#Skepticism_in_education

I have a feeling I'll find the problem in the fraction, it's not as simple as cutting the cake into 9ths, maybe one odd but equal slice too many (wow that sounds confusing). I'll think about it later.

Have you decided if it's finite or an infinite sequence? If it's definied by definition somebody please tell me.
 

DeletedUser

x = 0.999 r
10x = 9.999 r
10x-x = 9x

9x = 9
x=9

OR another explanation


9/9 = 1

1/9 = 0.111r
9x1/9 = 0.999r
0.999 = 1

Err, hold on......

x = 0.999 r -> OK, definition, setting this up
10x = 9.999 r -> Ok, both sides multiply by 10
10x-x = 9x -> err, NO! Below is what happens when you subtract x from both sides.

10x - x = 9.999 r - x
10x - x = 9.999 r - 0.999 r -> from line 1, definition
10x - x = 9 r
9 x = 9 r

Your last 2 lines are also incorrect when combine together

9x = 9
x = 9
Err, what? If anything, X = 1....
 

DeletedUser

Err, hold on......

x = 0.999 r -> OK, definition, setting this up
10x = 9.999 r -> Ok, both sides multiply by 10
10x-x = 9x -> err, NO! Below is what happens when you subtract x from both sides.

10x - x = 9.999 r - x
10x - x = 9.999 r - 0.999 r -> from line 1, definition
10x - x = 9 r
9 x = 9 r

Your last 2 lines are also incorrect when combine together

9x = 9
x = 9
Err, what? If anything, X = 1....
I think that proves that is thread is an.....EPIC FAILURE;)
this is like trying to say 2+2=9
 

DeletedUser

*Klonan's mind*
999999 too... many... 9s.... does not compute!
*Klonan explodes*
THE END
 

DeletedUser14280

Alright, we can be sure that:
a/a = 1.
...It's a basic rule of algebra and stuffs.

And we know that:
1/9 = 0.1
...In which the 1 in the decimal is recurring.

Now if we added 8/9 and 1/9 together:

This is what it looks like in decimal:
0.8 + 0.1 = 0.9

This is what it looks like in fraction:
8/9 + 1/9 = (8 + 1)/9 = 9/9

9/9 simplifies to 1 because a/a = 1.

So, it makes no sense, it's a complete, utter enigma, but it's true.

I like to think of 0.9 and 1 having a 1/∞ difference between them.
A theoretical difference, really.
 
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