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At 4/28/08 04:06 PM, CatherineElizabeth wrote: x = 0.9~

10x = 9.9~

10x - x = 9.9~ - x

9x = 9

x = 1

Therefore, 1 = 0.9~.

Not at all. Your proof loses validation since you've misused your variable.
Also, your premise 4 is off.

At 4/29/08 03:16 PM, n64kid wrote:

At 4/28/08 04:06 PM, CatherineElizabeth wrote: x = 0.9~

10x = 9.9~

10x - x = 9.9~ - x

9x = 9

x = 1

Therefore, 1 = 0.9~.

Not at all. Your proof loses validation since you've misused your variable.
Also, your premise 4 is off.

Welcome to page 1, i'm glad you could join us

Your my Slow Chemical

Here is another proof.

Validation of formula used in part b is here.

Part a can be shown by doing the first few values of k.

Part c is basic math.

What the fuck is part c meant to prove?

hey guys look, I just proved that 24.9 equals 1 by following the formula shown to us in part c of that picture!!!!!

You people who are posting "This doesn't make sense its wrong" make me sad. This is all so simple, and I think the tilde is messing you up.

0.999...=1

Observe:

(1/3) = 0.333...

3(1/3) = 3(0.333...)

1 = 0.999...

Caveat: 0.999...999 does not equal one. Only 0.999... does.

At 4/29/08 11:09 AM, BonusStage wrote: They're like the subatomic world in chemistry, except in math.

Chemistry is studying the bonds atoms make with each other using electrons. Subatomic particles is a branch in physics (Although chemical equations are applyed here also).

At 4/29/08 03:04 PM, Fyndir wrote:

At 4/29/08 02:56 PM, Glaiel-Gamer wrote: What the hell do you think a limit is?

Man, you people keep asking that.

I posted a definition in this thread for those of you who are a bit...slow.

I know what a limit is, I was asking what he thought it was cause he said that limits don't converge.

At 4/29/08 03:54 PM, Fyndir wrote: What the fuck is part c meant to prove?

hey guys look, I just proved that 24.9 equals 1 by following the formula shown to us in part c of that picture!!!!!

You're an idiot. He substituted the values from part A into part B to get part C

You didn't prove that 24.9 = 1, you proved that 24.9/24.9 = 1

At 4/28/08 09:48 PM, Glaiel-Gamer wrote: lim(x -> infinity) 1 - 1/x

This just means it's approaching 1, but never reaching it.

At 4/29/08 04:19 PM, Glaiel-Gamer wrote: You didn't prove that 24.9 = 1, you proved that 24.9/24.9 = 1

He didn't prove that 0.9 = 1, he proved that 0.9/0.9 = 1.

What's your point again?

At 4/29/08 04:20 PM, Mind-Edge wrote:

At 4/28/08 09:48 PM, Glaiel-Gamer wrote: lim(x -> infinity) 1 - 1/x

This just means it's approaching 1, but never reaching it.

Ok try this then

lim (x -> 4) x = 4

By your logic, that means that x is approaching 4 but never reaching it. Ya, that's what the limit means, however because you don't get a /0 effect at x = 4, then the limit to and the value of x at 4 are the same thing.

You don't get a 1/0 error in 1 - 1/x when x is infinity, therefore the limit of and the value at are exactly the same.

It reaches it at infinity. In order to deal with infinity in math, you cannot treat it as a concept, but must instead treat it as a number with its own special properties.

x can be any real number other than infinity (or 0) in this case

x/inf = 0

inf + x = inf

inf / x = inf

inf / inf = undefined

inf * x = inf

inf * inf = inf

inf / 0 = undefined

inf * 0 = 0

These definitions are standard and used in all upper level math courses (like calculus)

At 4/29/08 04:20 PM, Fyndir wrote:

At 4/29/08 04:19 PM, Glaiel-Gamer wrote: You didn't prove that 24.9 = 1, you proved that 24.9/24.9 = 1

He didn't prove that 0.9 = 1, he proved that 0.9/0.9 = 1.

What's your point again?

Look at his other 2 equations there.

Equation A was the definition of a repeating decimal series (for .999....)

Equation B was how to solve for an infinite series.

Plug equation A into equation B and you get his part C, which evaluated the infinite series as .9/.9, or 1.

Seriously, the only people that dispute the FACT that 1 = .999.... are people who have not reached or taken upper level math classes.

At 4/29/08 04:34 PM, Glaiel-Gamer wrote: Seriously, the only people that dispute the FACT that 1 = .999.... are people who have not reached or taken upper level math classes.

Or people who realise that just because a number continues forever doesn't mean it turns into a new number.

Your system is flawed, deal with it.

At 4/29/08 04:36 PM, Fyndir wrote:

At 4/29/08 04:34 PM, Glaiel-Gamer wrote: Seriously, the only people that dispute the FACT that 1 = .999.... are people who have not reached or taken upper level math classes.

Or people who realise that just because a number continues forever doesn't mean it turns into a new number.

Your system is flawed, deal with it.

No it doesn't turn into a new number. It's the same number to begin with

There are many different ways to represent the same number

1
.999....
9/9
I
1 + 0i
01
01.0
1.000
one
uno
0x01
sin(x)^2 + cos(x)^2

they are all the same number, just represented in different ways.

At 4/29/08 04:42 PM, Glaiel-Gamer wrote: No it doesn't turn into a new number. It's the same number to begin with

Except it isn't.

There is a .000...1 difference between .999... and 1.

At 4/29/08 04:34 PM, Glaiel-Gamer wrote: inf * 0 = 0

Nope, it's an indeterminate form because, and anyways, the limit by which you divide something by zero technically goes to infinity anyways, not zero. But this problem is impossible since you're thinking infinity is a number, which it isn't.

At 4/29/08 04:44 PM, Fyndir wrote:

At 4/29/08 04:42 PM, Glaiel-Gamer wrote: No it doesn't turn into a new number. It's the same number to begin with

Except it isn't.

There is a .000...1 difference between .999... and 1.

Wrong! If we were talking about 0.999...9 you would be right, but there is no terminating decimal. You have made one of the classic blunders!

Actually, I'm beginning to wonder if you're playing devil's advocate, or if you're just bored.

At 4/29/08 05:00 PM, AMP-d wrote: Wrong! If we were talking about 0.999...9 you would be right, but there is no terminating decimal. You have made one of the classic blunders!

If there's no terminating decimal then it's not a number.

Duh.

At 4/29/08 04:53 PM, BonusStage wrote:

At 4/29/08 04:34 PM, Glaiel-Gamer wrote: inf * 0 = 0

Nope, it's an indeterminate form because, and anyways, the limit by which you divide something by zero technically goes to infinity anyways, not zero. But this problem is impossible since you're thinking infinity is a number, which it isn't.

the * means multiply, not divide.

Anyway though, you HAVE to treat infinity as a number to solve certain problems.

i isn't a real number, there is no square root of 1, but it has use in mathematics nonetheless.

At 4/29/08 05:05 PM, Glaiel-Gamer wrote: there is no square root of 1

I meant sqrt of -1

At 4/29/08 05:09 PM, ChrisCrucker wrote: LEAVE 0.999 ALONE!!!

We won't bother nine-hundred-ninety-nine thousandths. It's 0.999... , also known as one, that we're worrying about.

At 4/29/08 05:04 PM, Fyndir wrote:

At 4/29/08 05:00 PM, AMP-d wrote: Wrong! If we were talking about 0.999...9 you would be right, but there is no terminating decimal. You have made one of the classic blunders!

If there's no terminating decimal then it's not a number.

Duh.

It is a number, more specifically a rational number, which can be expressed as a/b, where b is not equal to 0, or as any terminating or repeating decimal.

It's nice to know that we have enough intelligent people on Newgrounds that we can have discussions like this.

At 4/29/08 05:05 PM, Glaiel-Gamer wrote: the * means multiply, not divide.

oh ok

At 4/29/08 03:17 PM, Michael wrote: Welcome to page 1, i'm glad you could join us

Except no one addressed how stupid this thread is due to the fact that you DO NOT DERIVE 1=~.9

At 4/29/08 03:16 PM, n64kid wrote:

At 4/28/08 04:06 PM, CatherineElizabeth wrote:

x = 0.9~

10x = 9.9~

10x - x = 9.9~ - x

Let's FILL IN .9~ for the X.

10(.9~) - (.9~) = 9.9~ - (.9~)

That's 9.9~-.9~ = 9.9~ -.9~
Or 9=9

See how there IS NOT AN X THAT REMAINS.

X remains equal to .9~, and not 1.

Learn some algebra.

At 4/29/08 06:15 PM, n64kid wrote: Learn some algebra.

You only had no x's at the end because you replaced all of them. You don't have to replace all of them you know.

Oh and BTW learn some calculus.

At 4/29/08 06:21 PM, Glaiel-Gamer wrote:

At 4/29/08 06:15 PM, n64kid wrote: Learn some algebra.

You only had no x's at the end because you replaced all of them. You don't have to replace all of them you know.

To be consistent you do, otherwise you throw out the meaning of the whole proof.
Now go learn algebra you nit-wit, and thats coming from someone who knows calculus, analytic geometry, actuarial science, trig, abstract algebra (Algebra IV), mathematical logic, finite/infinite math, and topology.

My middle school education salutes you this day.

At 4/29/08 06:28 PM, n64kid wrote: To be consistent you do, otherwise you throw out the meaning of the whole proof.

It's completely legal to only substitute out a few x's, it doesn't change the meaning of anything

I.E.

x^2 = x^2, x = 4

16 = 16

It's EXACTLY the same as

x^2 = 16 (only substituting half of the equation)
(x is still 4 keep in mind)

Both sides remain equal, both sides are the same. What's wrong with that?

Now go learn algebra you nit-wit, and thats coming from someone who knows calculus, analytic geometry, actuarial science, trig, abstract algebra (Algebra IV), mathematical logic, finite/infinite math, and topology.

I know algebra, and I don't care what advanced maths you've taken (I've taken through calculus, and will be taking many more in college as my minor will be math), but I doubt you learned anything from those classes because you insist upon your wrong facts.

For the love of GOD! This topic recycles itself every three pages!

Man, you all need to get your definition of infinity sorted out. 1 is equal to 0.9 recurring, and arguing that you could add on 9's and it would only get closer but never reach is incorrect and absurd, because there are infinite 9's. Infinite is a whole different concept to finite, you can't use finite examples to represent infinity.
Also, infinitely close means 0.

At 4/29/08 06:51 PM, HeartbreakHoldout wrote: Man, you all need to get your definition of infinity sorted out. 1 is equal to 0.9 recurring, and arguing that you could add on 9's and it would only get closer but never reach is incorrect and absurd, because there are infinite 9's.

Uh-huh...

Infinite = endless.

If there an endless number of 9's it doesn't suddenly change the value, it's still less than 1. =/

At 4/29/08 06:45 PM, ReciprocalAnalogy wrote: For the love of GOD! This topic recycles itself every three pages!

I know, it's fucking hilarious. =D