3.14159265358979323846264338327950288

[ArdRhys4]

It isn't equal to one. It is =~= 1 (approx.). Technically, neither theorem is true because all it actually is is =~=(I don't know how to make squiggly equals xD). However, the idea is funny enough to let it slide ^^.

[SnakeEyes]

It isn't equal to one. It is =~= 1 (approx.). Technically, neither theorem is true because all it actually is is =~=(I don't know how to make squiggly equals xD). However, the idea is funny enough to let it slide ^^.

it is EXACTLY 1. not approx. I've found a wikipedia article about it, maybe they know how to describe it better: http://en.wikipedia.org/wiki/0.999...

[ArdRhys4]

It isn't equal to one. It is =~= 1 (approx.). Technically, neither theorem is true because all it actually is is =~=(I don't know how to make squiggly equals xD). However, the idea is funny enough to let it slide ^^.

it is EXACTLY 1. not approx. I've found a wikipedia article about it, maybe they know how to describe it better: http://en.wikipedia.org/wiki/0.999...

I have been pwned. I am ashamed. However, the wikipedia article was a fun read. Very interesting. (only read to the point that it said applications at which point I decided to stop before I was completely entranced .

[gothicorpunk]

It isn't equal to one. It is =~= 1 (approx.). Technically, neither theorem is true because all it actually is is =~=(I don't know how to make squiggly equals xD). However, the idea is funny enough to let it slide ^^.

it is EXACTLY 1. not approx. I've found a wikipedia article about it, maybe they know how to describe it better: http://en.wikipedia.org/wiki/0.999...

I have been pwned. I am ashamed. However, the wikipedia article was a fun read. Very interesting. (only read to the point that it said applications at which point I decided to stop before I was completely entranced .

wow

[Jwilson6]

1/9 = 0.11111....
9*(1/9) = 9*(0.1111....)
1 = 0.9999....

same theorem, different proof :p

Great thing about math, you can make what ever you want, no matter how contradictory it may be, and just call it a theorem.

Contradictory? There's nothing contradictory about 0.999.. (9 to infinity) being equal to 1.

This is isn't even close to being true.
The problem is in your first step

1/9 = .11111111..... is false you can take the 1's out as far as you want its still false.
1/9 ≈ .1111111... is true because the 'roughly equals to' symbol acknowledges that they're only close to being equal but are not actually equal. Using that symbol your whole argument will come out true but then their will no longer be anything contradictory about it.

[SnakeEyes]

This is isn't even close to being true.
The problem is in your first step

1/9 = .11111111..... is false you can take the 1's out as far as you want its still false.
1/9 ≈ .1111111... is true because the 'roughly equals to' symbol acknowledges that they're only close to being equal but are not actually equal. Using that symbol your whole argument will come out true but then their will no longer be anything contradictory about it.

1/9 is equal to 0.111.. if you continue putting in 1s up til infinity. And that exactly is needed to get the proof. If you round ANYWHERE, 1/9 would not be equal but approximately equal and you can no longer come to the same conclusion. But I've never suggested any rounding anywhere.

[Jwilson6]

Sorry I didn't realize they're was a second page to this. I just looked at the wikipedia article and its wrong.

Their most shocking proofs and the ones they use most often are those involving sequences and series'. The problem here is pretty much the same thing as my post before. Whoever wrote the article is trying to say that the value of a limit is the same as the value of the number. This is not true, when we say something like the limit as n goes to infinite of 1/10 to the n'th power is equal to 0 what were really saying is that as n gets infinitely large the value of 1/10 to the nth power approaches 0. This is basically saying that (1/10)^∞ ≈0 , the same as my post before. This is not saying that the number is equal to 0. Often times we use it like such because the difference is so infitesimally small that it has no real effect on any sort of application, but that is not saying they're the same.

[Barefoot]

Contradictory? There's nothing contradictory about 0.999.. (9 to infinity) being equal to 1.

This is isn't even close to being true.
The problem is in your first step

1/9 = .11111111..... is false you can take the 1's out as far as you want its still false.
1/9 ≈ .1111111... is true because the 'roughly equals to' symbol acknowledges that they're only close to being equal but are not actually equal. Using that symbol your whole argument will come out true but then their will no longer be anything contradictory about it.

Nope. 1/9 = .11111....

The only time 1/9 would be merely ≈ .111111... would be if you removed the ....

[Highlander]

um is the answer 2

[omlow]

.999 recurring = 1.0

this is factual

[Barefoot]

Easiest construct for me to prove it to myself was this:

1/3 = .3333....

1/3 * 3 = 1
.333... * 3 = .9999.... --> If you've got three thirds, it has to equal one.

It's sometimes easier to use fractions to grasp that .9999.... is just another way of expressing the number 1 in the decimal form.

[Caia]

This again? Really?

.999 recurring = 1.0

As my calc teacher said to those who didn't believe him after proving it 3 different ways: Deal with it.

[M2-Destroyer]

So essentially, what you are saying is 0.999 + 0.999 = 2?

... And not 1.998?

[SnakeEyes]

So essentially, what you are saying is 0.999 + 0.999 = 2?

... And not 1.998?

no,

0.99999.. (recurring) + 0.99999.. (recurring) = 2

[M2-Destroyer]

No, it would actually be:

1.999(Recurring) and when it finally reaches the last digit, which it will ... everntually, it will have an 8 on the end.

0.999 Recurring is still a number, you can't just change it because it's too difficult to comprehend.

[M2-Destroyer]

... And plus, if you do round it up, then it will have to be an approximation, because any other calculations done based on this approximation will be out.

[Moleman]

1.999(Recurring) and when it finally reaches the last digit, which it will ... everntually, it will have an 8 on the end.

Umm, no and no! If you properly understood the concept of a recurring number then you would realise that both of your statements here could not be further from the truth!!

[Frozen.Soul]

5 + 5 = 30

[M2-Destroyer]

1.999(Recurring) and when it finally reaches the last digit, which it will ... everntually, it will have an 8 on the end.

Umm, no and no! If you properly understood the concept of a recurring number then you would realise that both of your statements here could not be further from the truth!!

It's basic logic moley. In essence 9 + 9 does not equal 20.

[Caia]

No, it would actually be:

1.999(Recurring) and when it finally reaches the last digit, which it will ... everntually, it will have an 8 on the end.

0.999 Recurring is still a number, you can't just change it because it's too difficult to comprehend.

No. There IS NO LAST DIGIT. They keep recurring forever. It goes on for infinity.

Edit: Typo.

[M2-Destroyer]

Well fair enough, but you can't just call 0.999 recurring 1.

You just can't. The number 1 is 1. Not 1.1 recurring, not 0.999 recurring.

0.999 recurring is, and only can be called 0.999 recurring. Not 1, not 0.

[Moleman]

It's basic logic moley. In essence 9 + 9 does not equal 20.

Correct, 9+9 = 18.... however I was adressing these two points you made in your last post,

1.999(Recurring) and when it finally reaches the last digit, which it will ... everntually

It can never reach the last digit, it will continue, infinitely getting closer to the number 2.

everntually, it will have an 8 on the end.

Again no, the number is infinitely rounding up, not down.




I think its been mentioned earlier but the easiest way to understand it is by turning the decimal into a fraction, e.g.

1 divided by 3 = 1/3 or expressed as a decimal, 0.333...reccuring.

1/3 multiplied by 3 = 1.

0.3333...reccuring multiplied by 3 = 0.999...recurring or, to all intents and purposes, 1.

[M2-Destroyer]

Errr - Thats why we have fractions.

Sheesh - Problem solved.

[SnakeEyes]

It's basic logic moley. In essence 9 + 9 does not equal 20.

Correct, 9+9 = 18.... however I was adressing these two points you made in your last post,

1.999(Recurring) and when it finally reaches the last digit, which it will ... everntually

It can never reach the last digit, it will continue, infinitely getting closer to the number 2.

everntually, it will have an 8 on the end.

Again no, the number is infinitely rounding up, not down.




I think its been mentioned earlier but the easiest way to understand it is by turning the decimal into a fraction, e.g.

1 divided by 3 = 1/3 or expressed as a decimal, 0.333...reccuring.

1/3 multiplied by 3 = 1.

0.3333...reccuring multiplied by 3 = 0.999...recurring or, to all intents and purposes, 1.

Indeed:

1/3 = 0.3333..recurring
1/3 * 3 = 0.3333..recurring * 3
3/3 = 0.9999..recurring
1 = 0.9999.. recurring

so you can DEFINITELY say that 1 is equal to 0.9999..recurring

[M2-Destroyer]

No, no you can't!

There will always be a part of the digit missing!

0.999 recurring cannot be the same as one, simply because there is always a digit missing at the end which is required to complete the number, which would make it 1.

And as 0.999 recurring is an infinite number, it is impossible to add the final digit to make 0.999 recurring 1.

Therefore, 0.999 recurring is not the same as 1.

[Destructo]

s, you can see that all steps are correct. I will go through each one.

• 1: Since a == b,

Actually, you know what? It is wrong. You cannot divide by zero as this would make the entirety of the statement untrue (or at least undefined/infinity). That is why it is wrong. Jwilson is right^^.

Ya' think thats hard?

Who can do: 10 devided by 3 ?

It is wrong simply because A does not equal b to start with!
Step 1 is incorrect, therefor you cannot make a correct statement out of an incorrect statement.
the argument is moot.

[Barefoot]

No, no you can't!

There will always be a part of the digit missing!

0.999 recurring cannot be the same as one, simply because there is always a digit missing at the end which is required to complete the number, which would make it 1.

And as 0.999 recurring is an infinite number, it is impossible to add the final digit to make 0.999 recurring 1.

Therefore, 0.999 recurring is not the same as 1.

M2, you might just have to resign to the fact that your mind can't grasp this concept.

(.999.....) is EXACTLY equal to the number 1. You are used to the paradigm that numbers can only be expressed one way in the decimal form. There are actually many different ways. The reason it makes sense to you in fraction form is because fractions can only be expressed in one way.

There are no digits missing from .999...., there is no final digit.

I'll reiterate this simple math to explain - this is what everyone is trying to get through your thick skull:

1) 1/3 = .3333.... (there is no last digit)
2) 1/3 * 3 = 1
3) .3333... * 3 = .99999..... = 1

Steps #2 and #3 are mathematical equations expressing the exact same numbers. All that was done was substituting .333.... for 1/3 (which I hope you can agree .333.... = 1/3)

You may not have been schooled on advanced math using calculus - asymptotic numbers are peculiar, but .9999.... = 1 ; 1.99999.... = 2 ; 2.9999.... = 3 . There is no 'almost', they are the exact same number.

[Mua'Dib]

It's pretty straightforward. There are a number of methods to prove it. Some involve limits/calc and some don't.
My algebra teacher showed us the following proof.

X = .999999...(recurring)
therefore
10X = 9.999999...(recurring)
Therefore
10X - X = 9.999999...(recurring) - .999999...(recurring)
So we subtract and the recurring digits exactly cancel each other...
9X = 9
X = 1

[Caia]

Well fair enough, but you can't just call 0.999 recurring 1.

You just can't. The number 1 is 1. Not 1.1 recurring, not 0.999 recurring.

0.999 recurring is, and only can be called 0.999 recurring. Not 1, not 0.

Sure you can. We do all the time in math. Moreover, its correct.

[M2-Destroyer]

Well saying that 0.999 recurring is the same as 1, is like saying that the value of gravity upon the earth is 10, not 9.8