PsiPog.net

View topic - .999999 (repeating) = 1

PsiPog.net Forum Index » General Discussion » .999999 (repeating) = 1

Goto page Previous 1, 2, 3 Next

.999999 (repeating) = 1

Author

Message

Posted on Thu Dec 07, 2006 5:45 pm

Damien

Joined: 28 May 2006
Posts: 89

Sure, 1/3 = .33333333 and 2/3 = .666666666 but not matter how you look at it 3/3 will always = 1. Period.

Posted on Thu Dec 07, 2006 7:15 pm

sgtpsion

Joined: 13 Jan 2006
Posts: 425

I have to hand it to mattz. I was deliberately trying to trip you guys up. I actually managed to fool my Math 10 teacher with that 2=1 thing!

But seriously, good job. My dad taught me the proof I gave you guys, and he also told me where it became invalid, so I was quite aware of it. I just decided to leave it out to see how many n00bs would find the thread and think that every number is every other number. Evidently, Mattz found the thread and the article before n00bs posted that the proof was awesome.

Hurrah! We are winning the War on n00bs!

Posted on Fri Dec 08, 2006 2:59 am

Felix_the_Cat

Joined: 17 Apr 2006
Posts: 177

0.9999... = 0.9 + 0.09 + 0.009 + ...
= 9(0.1 + 0.01 + 0.001 + ...)
= 9(-1 + 1 + 0.1 + 0.01 + 0.001 + ...)
= 9(-1 + sum[n=0,inf]((1/10)^n))

sum[n=0,inf](r^n) = 1/(1-r), |r| < 1

0.9999... = 9(-1 + 1/(1-1/10))
= 9(-1 + 10/9)
= 9(1/9)
= 1

QED.

Oh, the wonders of calculus.

See Wikipedia: infinite geometric series for details and algebraic proof that the sum is indeed equal to 1/(1-r), |r| < 1.

Re: .999999 (repeating) = 1 on Fri Dec 08, 2006 7:57 pm

Fakiti

Joined: 18 Jul 2006
Posts: 336

sayspo wrote:

2.

1/3 = .3333333(repeating)

2/3= .6666666(repeating)

I don't like this method (the second one) because you're saying .3333(repeating) is equal to 1/3. it basically is but that's like saying .9 (rpting) is equal to 1. that's what you're trying to prove.

Posted on Fri Dec 08, 2006 8:04 pm

Zemeon

Joined: 25 Apr 2006
Posts: 269

derricktheone wrote:

I understand that zemeon, however, you're not only limited to cutting the space in half. I know it invariably happens, but if you have a fixed point, why can't you be right on top of that fixed point. Move from it, to another fixed point? I don't know, that one doesn't seem sound to me.

*Edit- That didn't really explain it any better to me tankdown.

Didn't seem right to me either! But that's like a famous mathematition's theory, but I forget who it was.

Re: .999999 (repeating) = 1 on Fri Dec 08, 2006 10:34 pm

Felix_the_Cat

Joined: 17 Apr 2006
Posts: 177

Fakiti wrote:

sayspo wrote:

2.

1/3 = .3333333(repeating)

2/3= .6666666(repeating)

I don't like this method (the second one) because you're saying .3333(repeating) is equal to 1/3. it basically is but that's like saying .9 (rpting) is equal to 1. that's what you're trying to prove.

I can prove that 1/3 = .33333..., and 2/3 = .66666..., in the same way that I proved that .99999... = 1 above, using infinite geometric series.

If you guys ever take second-year college calculus, you will learn about infinite geometric series and will be able to reproduce the proof I gave, which is actually one of the easier applications of series.

Posted on Sat Dec 09, 2006 12:48 am

Damien

Joined: 28 May 2006
Posts: 89

Didn't you read the wiki article? .9999999... isn't equal to 1, no matter how you look at it. 'Less you round.

Posted on Sat Dec 09, 2006 1:25 am

Felix_the_Cat

Joined: 17 Apr 2006
Posts: 177

Damien wrote:

Didn't you read the wiki article? .9999999... isn't equal to 1, no matter how you look at it. 'Less you round.

The wiki article was referring to the "proof" posted that 1=2, which is an invalid proof because it divides by zero. Going from (x+y)(x-y) = y(x-y) to x+y = y is dividing both sides of the equation by (x-y). Since we have a priori (before the proof) defined x=y, then x-y=0 and we are dividing both sides of the equation by zero, which produces an undefined result, and makes the proof mathematically invalid.

The proof that .99999... = 1 (or that .33333... = 1/3, or that .66666... = 2/3, or that .11111 = 1/9, or that .63636363... = 7/11, or any other repeating decimal equalling its fractional equivalent), by representing the repeating decimal by an infinite geometric series (which is an exact way of representing the decimal, not an approximation) and then using the properties of infinite geometric series to calculate the fractional equivalent of the decimal, is in fact mathematically valid, and is actually an integral part of mathematics today. If infinitely repeating decimals were not rational numbers, then I'm sure a lot of higher-level math would have to be reworked.

Just trust me on this one, ok? I've completed a second-level college calculus course. I'd bet ten dollars against a penny that you haven't. Hence, you don't know the mathematics necessary to read and understand my proof that .99999... = 1.

Posted on Sat Dec 09, 2006 3:27 am

mattz1010

Joined: 14 Jan 2006
Posts: 885

What I mean is, that page that I posted also has some fun stuff to look at.

Although it's not on there, the 0.9 repeating equaling 1 is still invalid proof in my eyes. They are two different systems, and translations cause errors.
(Decimal and Fractional)
Everything on that page though, is quite funny to look at.

Posted on Sat Dec 09, 2006 3:50 am

Felix_the_Cat

Joined: 17 Apr 2006
Posts: 177

Wikipedia; Proof that 0.999... equals 1

I rest my case.

Posted on Tue Dec 12, 2006 7:56 am

Lleu

Joined: 29 Apr 2006
Posts: 153

Tankdown wrote:

You know the number I like? I forget who made it, but its the numbers of "Beauty".

1,2,3,5,8,13,21,34

You can find this pattern in a flower. Itsnt that cool!! Very Happy

Fibbonacci (sp) sequence. As it approaches infinity, the quotient of the last two numbers from right to left approaches phi.

Posted on Wed Dec 13, 2006 10:44 pm

Tankdown

Joined: 10 Aug 2006
Posts: 688

Lleu wrote:

Fibbonacci (sp) sequence. As it approaches infinity, the quotient of the last two numbers from right to left approaches phi.

Ahhh I knew it was something starting with a F. I had it at the tip of my tounge! Thanks! Laughing

Posted on Thu Dec 14, 2006 3:30 pm

mattz1010

Joined: 14 Jan 2006
Posts: 885

I believe the correct sequence starts off with 2 1's.

1, 1, 2, 3, 5, 8, 13, 21, 34...

Posted on Thu Dec 14, 2006 8:24 pm

Lleu

Joined: 29 Apr 2006
Posts: 153

011

Posted on Fri Dec 15, 2006 4:47 am

JOHNNYBEGOOD

Joined: 17 Jul 2006
Posts: 354

sayspo wrote:

lol, but i am pretty sure my second method doesnt involve an error like dividing by zero. Smile

This man divided by zero. He is god.

Goto page Previous 1, 2, 3 Next

PsiPog.net Forum Index » General Discussion » .999999 (repeating) = 1

You must agree to the Terms of Service and Privacy Policy to view this website. Click here to contact the webmaster.