General

It does my math teacher showed the class but I don't remember how

[quote=xSuperNova]This is still...?[/quote]

This is still what? o.o

[url=http://www.youtube.com/watch?v=wsOXvQn3JuE]Hi.[/url]

I always think of it like this:
1/3 = .3333333333333
2/3 = .666666666
1 = 3/3 = .999999999
So 1 = .999999999
Le gasp!~

Also, we can do this using algebra.
Say x=0.999999
Therefore, 10x=9.999999
~Solve the system of equations by subtracting them from eachother
~~~~~>10x - x = 9.99999 - 0.999999
~~~~~~~~>9x = 9
~~~~~~~~~>x = 1

[quote=fraddddBS]No I'm not. I simply substituted "0.444..." for "x", like it was equal to in the first place.

Have you never used substitution or something?[/quote]

probably hundreds of times more than you did lol
and you're looking at the wrong thing
i was commenting on the way you did the subtraction of 10x-x=9x and not 4x
lol....

[quote=xSuperNova]I'm sorry if I wasn't clear, let me explain line by line:

x = 0.444...
10x = 4.444...
Nothing wrong with these

10x - x = 4
Still good
4x = 4
Turns out that 10x - x is actually equal to 9x, not 4x, so correct is
9x = 4
x = 4/9

Thus, you can apply the same method for an algebraic proof that "0.999..." is equal to one.[/quote]

frad you're retarded lol

i think of it like an asymptote. it never reaches 1.

[quote=gamemage3]this would what we mathematicians call circular argument.
how do you know 1/3 = .33333333333?

also @ above
whos to say, that
x = .999999999
10x = 9.999999999999

you're multiplying a real number to something that might not even be a real number? the operation cross can only be used between 2 numbers in the same field, and it must be defined clearly.

Assume we can represent numbers as a sum of infinite decimals.
ln2 = 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 - 1/8 + 1/9 ....
multiply both sides by 2 to get
2ln2 = 2 - 1 + 2/3 - 1/2 + 2/5 - 1/3 + 2/7 - 1/4 + 2/9 - 1/5

recollect terms with same denominator
2ln2 = (2-1) - (1/2) + (2/3-1/3) - 1/4 + (2/5 - 1/5) - 1/6 +....

2ln2 = 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 - 1/8 + 1/9 ....
ln2 = 2ln2
1=2

contradiction
therefore numbers and infinite decimals are not the same[/quote]
If you're a mathematician work it out yourself, stop showing off and asking basil.

[quote=Penguinland]No, and this is why

Write .9 as a fraction. It is 9/10, so if you had one object and cut it into 10 pieces, you'd have 1/10 left over when you took away .9 of it.

Next, write .99 as a fraction. It is 99/100. An object cut into 100 pieces would have 1/100 left over when you took away .99 of it.

Try this for .999. Fraction is 999/1000. As you can see, the more 9's you add the smaller the remainder gets.

So, if you are willing to write a very very long string of .9999999.... you would get closer and closer to the number being equal to 1.0. In fact, you can get as close as you want, no matter how close you'd like to be. However you would always, and I mean always, have a tiny bit left over.[/quote]

You say 1>0.999... but by how much?

For the convergence theorem, if we have an infinite series in the form sum(Cr^n) where the absolute value of r < 1, the series converges to Cr/(1-r)

0.999... = 9(1/10)^1 + 9(1/10)^2 + 9(1/10)^3+...
Since r<1, the series converges.

9(1/10)/(1-(1/10))=(9/10)/(9/10)=1

no because it will never reach 1

It's very close to 1 but not quite one.
As my teachers say to me all the time, don't over-think things.

[quote=uOnPeriod]Use mathematical logic to figure it out.
3 thirds of one = 1
A third = .333333
3 times .333333 = .9999999
....[/quote]

this would what we mathematicians call circular argument.
how do you know 1/3 = .33333333333?

also @ above
whos to say, that
x = .999999999
10x = 9.999999999999

you're multiplying a real number to something that might not even be a real number? the operation cross can only be used between 2 numbers in the same field, and it must be defined clearly.

Assume we can represent numbers as a sum of infinite decimals.
ln2 = 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 - 1/8 + 1/9 ....
multiply both sides by 2 to get
2ln2 = 2 - 1 + 2/3 - 1/2 + 2/5 - 1/3 + 2/7 - 1/4 + 2/9 - 1/5

recollect terms with same denominator
2ln2 = (2-1) - (1/2) + (2/3-1/3) - 1/4 + (2/5 - 1/5) - 1/6 +....

2ln2 = 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 - 1/8 + 1/9 ....
ln2 = 2ln2
1=2

contradiction
therefore numbers and infinite decimals are not the same

[quote=gamemage3]this doesn't prove anything lol[/quote]
Use mathematical logic to figure it out.
3 thirds of one = 1
A third = .333333
3 times .333333 = .9999999
....

[quote=uOnPeriod]1/3=.333
3/3=1
3x.333333=.99999
So on.[/quote]

this doesn't prove anything lol

1/3=.333
3/3=1
3x.333333=.99999
So on.

1>.99