.999999999999...

[Darco]

You want math

x = .9~
10x = 9.9~
9x = 9
solve for x,
x = 1
No this is wrong

.999999 can not = 1 because that means x/x MUST equal 1. Type .999999999999/1 or 1/.9999999999999 into your calculator and it will never come out to be 1.

Using that same calculator, divide 1 by 3. Then go back to the first page and edit your post.

[Vaati]

I like this topic. [/not sarcasm]

.999 repeating I believe is 1. I'm not going to say why because it has already been said multiple times.

[KOH_Church]

if rounded...to any tenth and beyond will always = 1 but if rounding is not announced the number will remain .9 to the inf.

[Tural]

if rounded...to any tenth and beyond will always = 1 but if rounding is not announced the number will remain .9 to the inf.

It is equal to 1 without rounding.

[[cc]z@nd!]

at first I didn't think they were equal, but now I suppose they are... and now i'm confused...

anyways, the algebra seems to support it, but in everyday use, you simply can't say they are equal. i wrote a quick program to try this out, although i'm afraid i might be making an assumption on how floats in C++ work, but regardless, it says they're inequal. like how if you payed off 99.999...% of your monthly car payment, it's likely they'll still ask for that last bit of money from you.

[Tural]

You can not pay an infinite decimal sequence. You would be paying a whole number if that was even possible, which it isn't, because the infinite sequence equals 1. The program is not correct, the calculator is not correct, and whatever other mechanical device comes up that says .9~ != 1 is not correct, the mathematics are correct.

[Dalek]

But you would still be left with 0.00[inf]01 as a remainder.

[Tural]

You can't have a remainder from an infinite sequence. You can not use an infinite sequence like that. You're making it a real number, which it is not. It is equal to 1, which is the only situation in which it can be presented as a whole number. It can be used to calculate its own value, but it can not be used to calculate another value. You can't subtract an infinite sequence from a whole number, as you would never reach the end, where you would find what remains. It is impossible to do so. So no, you would not have that as a remainder. That is factually incorrect.

[neodos]

This is false, 0,99999999999999999.....

Is not equal to 1, ok it's really near from 1 but it's still not, theoricaly 1.

Also why this, stupid, question?

[jks]

You can't have a remainder from an infinite sequence. You can not use an infinite sequence like that. You're making it a real number, which it is not. It is equal to 1, which is the only situation in which it can be presented as a whole number. It can be used to calculate its own value, but it can not be used to calculate another value. You can't subtract an infinite sequence from a whole number, as you would never reach the end, where you would find what remains. It is impossible to do so. So no, you would not have that as a remainder. That is factually incorrect.

Indeed, since the remainder of an infinite sequence such as .999... would inevitably have a finite ending, and thus contradict the fact that it's an infinite sequence in and of itself.

[Tural]

Is not equal to 1, ok it's really near from 1 but it's still not, theoricaly 1.

Theoretically, not factually. In theory, it would not be 1, but this isn't theory, it is fact. It has been proven. You're just ignoring the evidence based on your own preconceived notions.

I laugh at the ratio of this.

[FleetAdmiralBacon]

.9999999... = 1 - 1/∞
1/∞ = 0, by definition.
.9999999... = 1 - 0
.9999999... = 1
there's also the 1/9 explanation.
1/9 = 0.1111111 repeated
2/9 = 0.2222222 repeated
3/9 = 0.3333333 repeated
...
9/9 = 0.9999999 repeated = 9/9 -> 1/1 = 1

[Philly]

*Cough* wtf is this topic about.
I would rather someone pay me 1 pound for something than 0.999... pounds. Therefore they are not the same. However, I could just 'imagine' that they were the same.

[Tural]

Therefore they are not the same.

Wrong, because they are the same. If someone was paying you an infinite .9 decimal sequence, they would be paying you a whole number.

What is with people and using the broken, non-mathematical logic to analyze a mathematical situation? That logic is broken. Applying it to the real world is making you wrong. Factually, proven, 100%, it is equal to one. Why are you rejecting the proven equations shoved in your face over and over?

The ratio of people who are correct to the people who merely think they are is astonishing.

[Philly]

I think you're seeing this from too much of a 'philasophical' point of view, for want of a better phrase. If 1 and 0.999... were the same, they would have the same the same value, which they do not.

[Tural]

I think you're seeing this from too much of a 'philasophical' point of view, for want of a better phrase.

You are being philosophical. You are using real-world situational logic. We are using math. We are using facts. You are using assumptions.

If 1 and 0.999... were the same, they would have the same the same value, which they do not.

Yes they do!

[shadowkhas]

This is counterproductive.

.999999999.... is 1. Are we done yet?

[Tural]

We need to be. I'm waiting to lock this, but jks said no. =/

[Philly]

If 1 and 0.999... were the same, they would have the same the same value, which they do not.

Yes they do!

No they don't!
We could go on like this for ages, but I think I'll leave it here, to be honest....

[jks]

If 1 and 0.999... were the same, they would have the same the same value, which they do not.

Yes they do!

No they don't!
We could go on like this for ages, but I think I'll leave it here, to be honest....

Explain to me why they don't equal each other. Are you saying 1/2 and .5 are not the same number because they aren't the same? Are you saying that 1/4 and .25 are not the same number?

.999... and 1 are two of the infinitely many ways to symbolically express the same exact idea.