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2004-12-17 23:54:20
Last author: Kayne
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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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2004-12-16 [windowframe]: Your maths is flawed kayne, Templar is absolutly right, 1/3 does not equal exactly o.33333 recurring. That's why good mathematicians prefer using 1/3 - because it's entirely more accurate than 0.333333 can ever be.

2004-12-17 [Aradon Templar]: w00t! *knew it* I lobe you Silvie ^___^

2004-12-17 [Aradon Templar]: Ooh, once, using more 'fundamentally flawed' ideas, I proved that x/0 = infinity :) Although, my teacher later pointed out that what I did actually proved that x cannot be divided by 0. Go figure :P

2004-12-17 [deus-ex-machina]: w00tness! now i know silvie and templar agree i have no problem in making the following statement: "HAHAHAHAHAHAHAHAH!".

2004-12-17 [windowframe]: :P Yeah, If I remember, the reson the 'all numbers are equal to zero' theorem is rubbish for the same reason (not being able to divide by 0) to somoen who doesn't really know maths - it looks plausible, but to those who know maths, you can see the flaws O.o Hpwever, it's still funny stuff. :P as long as you don't take it seriously

2004-12-17 [Kayne]: Silvie you are wrong, deal. 0.33... = 1/3 - It is just hard to write 0.333... cause that is kind off hard to write.

2004-12-17 [Kayne]: And if don't believe me: Here some non maths facts cause you don't tend to believe the maths. My mathteacher says it's true. My Fysicsteacher says it's true. On university - people who study math - learn this proof as true. Do you need more? Need some more math? sure: 1-0.999... = what?

2004-12-17 [deus-ex-machina]: 1-0.99999.... = NOT 0. Come on Kayne, what kind of credible sources are teachers? :) Of course I need more - I need a credible source from somewhere which says this is right.

2004-12-17 [windowframe]: yeah - we need a source that we can consult - for all we know, you've just sat their and bullshitted to us, face it kayne, your wrong, and by constantly making such big fuss about it, your making it so much harder for yourself when you finally realise it's wrong...

2004-12-17 [Kayne]: I was asking what is 1 - 0.999...

2004-12-17 [windowframe]: lets re-do Kayne's calcuation w/o the x. he says 'x = 0.999...' being as we can't use the whole of a recurring number, we'll just use '0.99999' so... x=0.99999, x 10 = 9.9999. - 0.99999 = 8.99991... oh dear, we seem to have encountered a problem.

2004-12-17 [deus-ex-machina]: and I told you it's not 0. Because you're saying 1 = .999... so 1 - .999... = 0... but it doesn't. Because there's something about 0.999 recurring that doesn't make it 1. So no matter how close it is to 1, it still ISN'T 1!

2004-12-17 [windowframe]: And for the record, Silvie is a nickname - nicknames are generally used only by friends - being as you blocked me from messe, and ended the relationship on ET, it's obvious that you don't want to be my 'friend' so don't call me Silvie.

2004-12-17 [deus-ex-machina]: and silvie did the math which i couldn't be bothered to do :P

2004-12-17 [deus-ex-machina]: OOOOH, I JUST CALLED HER SILVIE! *glomps her friend* ...sorry, LMAO

2004-12-17 [Kayne]: Oke SilverFire - You use a not)infinte row and those things just work differently. The 8 and the 1 will never appear. A finite row has no ending so therefore all numbers after the "." are the same. Do you get this? else withsomething else: Which numbers are more: the numbers who can be divided by 2 or numbers who can be divided by 1. ( And i mean numbers bigger then 0 )

2004-12-17 [windowframe]: "It seems to me that people are often too quick to dismiss the idea that these two numbers might be different."IS what people on the web have to say about this calculation

2004-12-17 [Kayne]: The first? you mean 10x = 9.999...?

2004-12-17 [windowframe]: And as to te one Templar mentioned, which you jump on: This argument gets its force from the fact that most people have been indoctrinated to accept the first equation without thinking."

2004-12-17 [Kayne]: No - You don't think at the equation. Cause it's an infinite number you can mulptiply by ten and the endless numbers after 0 stay the exact same way as they were before.

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*

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