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2004-12-17 23:54:20
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0.999... = 1

?

Yes

Why?

See below.




x = 0.999....

10x = 9.999...

10x - x = 9

10x - x = 9x

9 = 9x

1 = x

1 = 0.999...




Allow me to give an extra proof.

ormula:

I) 1+x+x^2+x^3.... = 1/(1-x)

if the absolute value of x is smaller than 1.

We can use this also as:

II) x+x^2+x^3.... = 1/(1-x) - 1


in our case:

0.999.... = 9/10 + 9/10^2 + 9/10^3 + .... =
= 9*(1/10 + 1/10^2 + 1/10^3 + ...) =
= 9*((1/10) + (1/10)^2 + (1/10)^3 + ...) =
(according to the formula II)
= 9*{1/[1-(1/10)] - 1} =
= 9*{1/[9/10]-1} =
= 9*{10/9 - 1} =
9*{1/9} = 1




As you probably know I didn't created this one myself. :p
Copy/past all the way.

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2004-12-17 [windowframe]: exactly - You have been indoctrinated to accept the first equation w/o thinking, when in fact, you should be thinking very hard, because, as templar pointed out, 1/3 is not exactly equivalent to 0.3* If we do the equation w/ a value that is actually equal to 1/3, (lets say 2/6) This happens: 1/3 = 2/6 , x3 = 1 = 6/6 ... 1 = 1 *gasps of shock*

2004-12-17 [deus-ex-machina]: it's wrong.

2004-12-17 [windowframe]: If you knew anything about Hackenstrings, then your entire proofs would break down - but I suppose you'd dearly love to remain ignorant of something which could totally destroy this crap, wouldn't you?

2004-12-17 [Kayne]: Nothing that you say can make this proof go wrong cause it is sollid. But introduce me anyway. And I would prefer if you stopped calling it crap cause while it is clear that you are telling crap.

2004-12-17 [windowframe]: *L* First point, this is 'non-crap' in yours eyes only - it is not 'obvious' that I am talking crap, you just don't want me to be right. Can you image the quantity 1?

2004-12-17 [Kayne]: 1 = 1 Yes I can. *Holds one finger up*

2004-12-17 [windowframe]: now hold up 0.9 recurring fingers. No, that's not one finger again, it's an infinite number - hold up your infinite finger, then. Ah wait - you don't have one, this could be a problem.

2004-12-17 [deus-ex-machina]: It's so solid no one believes you and you can't produce any evidence to show the obvious inaccuracies are actually acceptable?

2004-12-17 [Kayne]: Yes - an infinite recurring 0.9 finger = 1 finger. *Holds finger up* See SilverFire - you are taking math in to rl. That is not the thing I'm trying to say - it is a common "proof" that 0.99... = 1 but it doesn't work. Cause when we say that a 0.9recurring finger = 1 finger you say that is impossible. And then you ignore the math- proof.

2004-12-17 [windowframe]: I told you *not* to hold up one finger, so what do you do - hold up one finger. Who wants to comment on the IQ levels of the author of this page? I'm not *ignoreing* the maths proof actually, I'm disproving it - you just won't let me.

2004-12-17 [Kayne]: How helps disproving it by going in to "rl" while this is clearly something that just doesn't work in real life.

2004-12-17 [windowframe]: Lets put this more simply for you. 1 is a single number, a single digit, a definable quantity, 0.9* is not a single number, not a single digit and not a definable quantity.

2004-12-17 [Kayne]: Why isn't it definable? If you write it as 1 you habe the same number. Ask your math teachter for my sake.

2004-12-17 [windowframe]: *already did*. *sigh* again, right... 1 = 2. disprove it.

2004-12-17 [Kayne]: No - Fifst proof that it is. Then I will point out your obvious mistake. What did he say?

2004-12-17 [windowframe]: I just proved it did, look 1 = 2. They're the same just accept it. look *holds up finger* one, *holds up finger again* two. If that proof works for you, then it sure as hell works for me.

2004-12-17 [Kayne]: See Silvie you are talking Bullshit and this time you know it - don't waist my time.

2004-12-17 [deus-ex-machina]: actually, she's being perfectly reasonable. in the last few comments she was just showing you how illogical you have been in explaining your 'fact'.

2004-12-17 [windowframe]: That's Still SilverFire to you, bub. No, I am not talking BullShit, no, I am not wasting your time, to be frank, you're acting like you're stuck up your own arse - the nature of infinites, actual or potential is highly philosophical - therefore, different people have different opinions on how they can be handled. Deal. My opinion is different to yours, that doesn't mean it's bull, or irrelevant, it means it's different. If you can agree to disagree w/ **ppo, why is it so hard for you to agree to disagree w/ us? Why do you constantly have to try and shove this down our throats?

2004-12-17 [Kayne]: Cause you are - from a mathematiques ( How do you spell that ) point of vieuw - Wrong :/ And I just love stuffing that down your throat

2004-12-17 [deus-ex-machina]: I love how you're ignoring me. 0.9* does not have to be 1. Otherwise why would 0.9* need to be expressed at all if it could just be implied as 1? There's a reason why 0.9* is 0.9* is shown as such and not 1 because they're not the same freaking thing.

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