[split] 0.999... equals 1

[Darwinian]

1 / 3 = .33r

3 * .33r = .99r

.99r = 1

Seems obvious to little ol' me..

[Violet]

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Then the universe becomes nothingness, which is equal to itself (0 = 0 | | 1 = 1)... therefore righting the inequality.
-OR if it were 1.001-
The universe becomes a single ever compounding mass... creates a singularity... which then rights the inequality.

No it doesn't. 1 is provably 0.999... (reoccuring)

Here is my favourite proof:

x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 1

So x = 0.999... = 1

Fine the error in my math if you want, but you won't since this thing has been known by mathematicians for years

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10X - X is the same as 9X. You agree with this? Then you will find that your mathematical "proof" just evaporated.

[Retorth]

I stand corrected.

Let us agree to disagree and move on....to new topics!

but this isn't a matter of opinion. Its a matter of established mathematics which if ever proved wrong would spell fame and fortune for who ever proves it wrong. 6 pages in, the effort to prove it wrong seems to be giving up. No fame or fortune for anyone I suppose.

For the record, I do accept (not that you can't technically) the math. In fact, I've been researching on it. Just so you understand my stand here lol

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10X - X is the same as 9X. You agree with this? Then you will find that your mathematical "proof" just evaporated.

How does "10X -X = 9X" evaporate the mathematical equation?

[Violet]

Because you get a different answer when take 10X - X = 9X (with x= .9^)... and when you simply multiply by 9X.

Ill show you with whole numbers:
5*10 - 5 = 45
5 * 9 = 45

However, with .9^:
10X - X = 9X=9 (x=1 using adrian's 'proof')
9X = 8.9^1 (x=.9^)

This has come up with a different answer (entirely) from x=1. These two equations should in theory give the same answer, but they do not.

[Retorth]

I don't get your calculation...but I do know that you cannot compare this mathematical equation with whole numbers because thats the beauty of this. It is based on "infinity". It's like trying to compare a cat and a dog. They are both animals but they are still different in that one is a cat and the other is a dog. You have to look at it in its respective perspective.

Look at it in this way then:

1/3 = 0.333333333333333333(infinite3) <-- This you can obtain through any standard calculator of course.

2/3 = 0.333333333333333333(infinite3) + 0.333333333333333333333(infinite3)
= 0.666666666666666666(inifinite6)

3/3 = 0.666666666666666666(infinite6) + 0.333333333333333333333(infinite3)
= 0.999999999999999999(infinite9)

Therefore,
3/3 = 0.999999999999999999(infinite9) and 3/3 = 1

so 0.9999999999999999999(infinite9) = 1


Its actually what Eilonwwy showed in an earlier post, so credit to her on this.

I think the reason you don't seem to get it is because you look at it as a finite number of "9"s at the end. If its a finite number then yes this whole thing is inaccurate.

E.g.

If X = 0.99

10X = 9.9

10X - X = 9.9 - 0.99 = 8.91

And this will be the same no matter how many different combinations of 9's you use. However, like what Adrian has been saying, if the number of 9's is infinite, even if you multiply 0.999999999999999(infinite9) by 10 or by 100 for that matter, the number of .999999999(infinite9) never changes because its infinite. It keeps on going.

[Tiberius]

To believe that 0.999... does not equal 1, you have to believe the following:

1) That 0.333... is not an accurate representation of 1/3 (and it is, any higher number and you don't get 1/3, same for lower numbers)
2) That 3 x 3 does not equal 9, and from that that any decimal form of 0.333 (any number of threes) multiplied by 3 does not equal 0.999 (with the same number of nines).
3) That there is a number in between 0.999... and 1, even though 0.999... is by definition infinitely long and 9 is the highest digit in the decimal system.

So effectively, you have to reinvent mathematics.

Please then,

1) Give me a better representation of 1/3 in decimal form.
2) Show me that 3 x 3 does not equal 9.
3) Tell me the number in between 0.999... and 1 (and don't say "an infinitely long number of 0s with a 1 on the end" because I have already shown how that is simply not mathematically possible)

* Tiberius loves watching people try and argue established mathematical proof when they clearly do not understand the concept of infinity.

[fr0d0]

0.999r never becomes 1 to infinity because the two never ever touch. The never ever bit is a known. They get closer and closer together but never touch - this is the point - never

Those proofs are laughable because they ignore this. Yeah sure it's theory, and it's 'as good as' 1, but it never is.

Adrian stated two incompatible statements:

By definition two numbers cannot be the same if they are different amounts

0.999... is provably equal to 1

1/3 is accurate
0.3333r isn't accurate

[Violet]

1. You cannot get more accurate, because you could not divide 1 evenly into three. 1/3=.3^ is an approximation based on that we cannot get any closer without overshooting one, but neither can we reach one.
2. 3 X 3 does = 9, and .9^ still doesn't equal one. I do not see why I would have to doubt this.
3. If that is not mathematically possible, then infinity was not possible to begin with Infinity + 1 is still infinity... it is just an added one on top of the initial concept.

I do not see how you reckon that .9^ is any more valid than the .0^1 long gap .9^ requires to equal one. There are an infinite amount of zeros between that decimal and that one... just as there is an infinite amount of nines following the decimal.

* Saerules dislikes watching the person who proved that 2 was prime be drowned by 'mathematicians' who did not want to establish the truth against what they'd thought right for years...

Establishment does not make something 'right', and mathematical establishment has been proved wrong before. Some of us understand the concept of endless... and justly realize that endless .9^ by definition means that it never becomes one. If .9^ were equal to one... then .0^1 would be equal to zero. Those numbers are separated from both one and zero by a mere .0^1... but that does not mean that the .0^1 is not there.

[Tiberius]

0.999r never becomes 1 to infinity because the two never ever touch. The never ever bit is a known. They get closer and closer together but never touch - this is the point - never

Except that there is no number between the two, so they do touch. They are the same number.

Those proofs are laughable because they ignore this. Yeah sure it's theory, and it's 'as good as' 1, but it never is.

The mathematical community is laughing at you as you laugh at us. It's not theory, it's provable mathematical fact. I showed two proofs that have not been refuted.

Adrian stated two incompatible statements:

By definition two numbers cannot be the same if they are different amounts

0.999... is provably equal to 1

Yes, and 0.999... and 1 are not different amounts. Note the difference between the words "numbers", "digits", and "amounts". The digits are very different, the amounts are not.

1/3 is accurate
0.3333r isn't accurate

So what decimal number is accurate? You can't just state that 0.333r isn't accurate without giving a valid decimal number to replace it. I guarantee, anything you think of won't be equal to 1/3.

Oh, and it's actually fractions that are inaccurate. Can you tell me the fraction for pi? No. No irrational numbers have fractions (it is the very definition of an irrational number).

[fr0d0]

They aren't the same number because there's always a gap to infinity. They cannot meet.

Those proofs are obviously flawed. They ignore the missing link. Is this April fools day? Where do I sign up for a labotomy?

Right - 'amount'. By their logic - I could give you 10,000 x 99p in exchange for your £10,000 and be £100 in profit. Wanna do some money exchanges?

Decimal numbers can't always be accurate. This proves it.

Pi is a decimal summation so is more accurate than 22/7