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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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2004-12-17 [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.

2004-12-17 [windowframe]: No, apparently you are unaware of how closely philosophy and maths are related - infinity is one of the only areas of maths where you can't have the black and white areas that you are trying to trace. You have your opinion, I have mine, You have calculations to prove it, so do I. Again, I empahsise the need for you to learn to deal. Besides - iippo doesn't agree w/ you either - why aren't you stuffing it down her throat?

2004-12-17 [Kayne]: iippo has feelings who can be broken. ( Low joke I know ). You have calculations to prrof your thingy? 0.0 *searches*

2004-12-18 [Aradon Templar]: Dude, kayne, Deus just proved you wrong. 1 doesn't equal .9*, because of the quite noticable difference between the appearances of 1, and .9*. How does one write decimals into fractions? One takes the number in the decimal, and puts it over 10^x, where x is how many places the decimal goes to. SO: .9* = (9*/10*). See? Now, kayne, 1 = x/x. If x were to equal 9*, then the denominator would have to be equal to 9*. But it isn't. It is 10*. Thus proved wrong.

2004-12-19 [Kayne]: See Templar first off al every number that doesn't have an infinte line of numers behind the . can be written as an infinite line. Example: 0.52 can be written as 0.5199999... Those 2 numbers have the exact same value. Now for the other part of your comment: I habe no idea what the hell you are saying. o.0 Just to clear thing out: 1/1 = the second 1 = denominator? // Fractions = ? // And one a final note: 10^x => 10^.9* = .9x // <= Is that what you were saying?

2004-12-19 [Kayne]: And one oher thing: If you are planning on never believing me, let me know then I'll stop trying. Or better ask your math-teacher and tell me what he thinks

2004-12-19 [Kayne]: And one oher thing: If you are planning on never believing me, let me know then I'll stop trying. Or better ask your math-teacher and tell me what he thinks.

2004-12-19 [Aradon Templar]: I'm out for winter break :) But I am going to ask when I get back. As for your other questions, the top number in a fraction (where you have one number underneath another number, and divide like that) is a numerator, and the bottom number is the denominator. So, 12 over 15 is a fraction. And the twelve is the numerator, and the 15 is the denominator.

2004-12-19 [Kayne]: Danke - Just another question. How much would 1 - 0.999... be?

2004-12-19 [deus-ex-machina]: not 0 :P

2004-12-19 [windowframe]: 0.0*1 1. Your first answer doesn't work for someone who doesn't believe your theory - it's only good for those who already accept it; and therefore useless as evidence. You can't say that "Those two numbers have exactly the same value" and just expect us to accept it - becuse obviously, we don't. You need to provide some proof that in our opinions is decent. You haven't.

2004-12-19 [Kayne]: *points to wikisubstance* That is the evidence. See SilverFire - there is your mistake. 1 - 0.9* cannot be 0.0*1. The * = infinite so that would mean that the 1 never comes. And therefore 1 - 0.9* = 0

2004-12-19 [windowframe]: on the contrary - there is no mistake. It just means that the 1 is part of the infinity. You and I have different opinions of the nature of infinity, and neither can be really proven - so you'll just have to accept that you aren't wrong - but neither are we.

2004-12-19 [deus-ex-machina]: but neither would that value that would make 0.9* exactly 1... there's always going to be a difference between the two numbers that doesn't give an end product of 0.

2004-12-19 [Kayne]: :/ Oke - I'll deal with the fact that you think you aren't wrong.

2004-12-19 [windowframe]: No. Don't deal with that fact, Deal with the fact that we aren't - and neither are you. Or is that simply beyond your ability? To accept that two opposing views aren't wrong? That's where your lack of respect becomes plain show. That even when you act like your trying to be reasonable, your pathetic attempt at arrogance is still shown.

2004-12-19 [Kayne]: Now SilverFire - If you can explain to me when something in math can't be sure thus I will accept the fact that I might be wrong.

2004-12-19 [windowframe]: I'm not asking you to accept the fact that you might be goddamned wrong you loon. I'm askin you to accept the fact that both points of view are plausible. What exactly, is so hard for you small little mind to comprehend about that? And for teh record - if your English gets any worse, don't expect a reply - it's barely understandable as it is.

2004-12-19 [Kayne]: And yet again - you don't reply to a direct question but you attack both my grammar and other meaningless stuff. But oke - I'll accept the fact that both points of view are plausible if you can explain how there can be a mistake in math.

2004-12-19 [windowframe]: Well, to be fair - how can I reply to a question I can't understand because of the English? You critisise me for asking you to write better - but I asked so I could actually answer the damn question. Decide what you want already, an answer, or no comments on your English. PLus - you didn't even ask a question - *can see no question marks in recent comments*

2004-12-19 [Kayne]: If you can explain to me when something in math can't be sure thus I will accept the fact that I might be wrong. Looks to me that I asked for an explanation. Ow but wait - you would probably don't want me too accept it. Anyway again no answer to my indirect question. How the hell is it possible that there can be a mistake in math?

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