Forums → The Tavern → 0.999... = 1

I understand what you mean, but this is really complicated! O_O
I do not agree that 1 is 2, but i agree that 0.999999999999 is 1!

I remember that my old maths teacher proved to us that 1=2 using algebraic quadratic equations. Buut u have never heard of this, interesting.

Ahh, here we have the omplications of our math system... 1/3 is approximately 0.333, however it's never truely 1/3. Noting 1/3 down as one number and have it completely accurate is simply not possible!

Besides, when adding these numbers, you have to remember the significance of those numbers - 0.333... is acually 0.3333333333 as well, and the fourth number of 0.9999 needs to be rounded up, making it 1.

But yeah, tough subject

basically, what I'm proving is that when you cut a cake into fractions, you have to remember there is some cake stuck to the knife. If you collect the cake from the knife after enough cuts, you can make another slice.

I do not agree that 1 is 2

I remembering looking at some work by a guy that had spent decades on a hugely complicated equation thats sole purpose was to prove that 1+1=2. I love that about the human mind that some can sacrifice huge parts of their lives to prove something most people take for granted fromt he age of about 5. Like PixelSmash said in most cases infinite numbers will be rounded.

I found the algebraic way of roving 2=1

a = x [true for some a's and x's]
a+a = a+x [add a to both sides]
2a = a+x [a+a = 2a]
2a-2x = a+x-2x [subtract 2x from both sides]
2(a-x) = a+x-2x [2a-2x = 2(a-x)]
2(a-x) = a-x [x-2x = -x]
2 = 1 [divide both sides by a-x]

You can't do that Woody. a - x = 0 so your dividing by 0. Of course the answer will come out wrong.

Ow, math... But yes, once you look at the details the questions pops up...

But it is because of approximates. Two thirds will be rounded up to 0.6666...6667 unless you choose to write an infinite number. Then adding the next third with the same amount of decimals will make it one...

I agree on your thinking, though.

The problem is obvious. We have no Decimal value that is exactly equal to a fraction.

Here is a different equation that proves 1=2. It uses substitution intead.

consider
x = y -> start with this assertion

x*x = x* y -> now multiply both sides by x

x^2 = xy -> x^2 is x squared

x^2 - y^2 = xy - y^2 -> subtract y^2 from both sides

(x - y)(x + y) = y(x - y) -> factor both sides

notice that (x - y) occurs on both sides so we
can cancel or divide both sides by (x - y)

thus we have

x + y = y -> after cancelling the (x - y)

but our original assertion we have x = y
thus substituting we have

y + y = y
or
2y = 1y

cancel the y on both sides

2 = 1

Q.E.D.

x - y = 0

You're still dividing by Zero.

The problem is obvious. We have no Decimal value that is exactly equal to a fraction.

It's the same in binary. If we were to change the numbering system to fix this one problem, then other problems would come from it. Basically, decimals are not useful past the 3rd significant number anyways.

Also just to let you know, Tangent is the reason you can't divide by zero. There are four answers to divide by 0:

Pos Infinity
Neg Infinity
Zero
Null

2 = 1 [divide both sides by a-x]