Why 0.999~ = 1

[CatherineElizabeth]

x = 0.9~

10x = 9.9~

10x - x = 9.9~ - x

9x = 9

x = 1

Therefore, 1 = 0.9~.

If you know any other proofs for 1 = 0.9~, please share them, or if you wish to challenge the validity of my proof or the statement that 1 = 0.9~, feel free to provide a critique.

[UfaKefe]

Has this not been discussed some time ago?

[solardave]

I don't really care.

[simple-but-sandy]

Actually, I prefer the logic:

1/9=0.1111111
2/9=0.2222222
...
8/9=0.8888888
So,
9/9=1=0.9999999

It's all bullshit if you look hard enough...

[Darkstrategy]

I think .99~ = 1 because no one really cares about the .00...1 to bother.

[Biscuit-Boy]

Thanks! I would never have known because I am from the South and don't believe in education!

Not that South. Even further.... yeah thats right, past Alabama!

[Murloc119]

To much algebra pisses me off...

[LampFace]

WTF does ~ mean?

[CatherineElizabeth]

At 4/28/08 04:11 PM, LampFace wrote: WTF does ~ mean?

Repeating. I can't make the repeating symbol normally used in Algebra (the bar over the number), so I use the next best thing, the tilda sign.

So 09.~ is 0.99999999999999999999999999999999999999 99999..... and all the way to infinity.

[Evark]

At 4/28/08 04:06 PM, CatherineElizabeth wrote: 10x - x = 9.9~ - x
9x = 9

That part right there, in it's wrongness, is what makes your proof possible. 10x - x = 10.

If you know any other proofs for 1 = 0.9~, please share them, or if you wish to challenge the validity of my proof or the statement that 1 = 0.9~, feel free to provide a critique.

Regardless, I've seen proofs that do it without mistakes such as the above. I don't agree with them, they simply take advantage of the human inability to express the infinite to prove something stupid. .9~ approaches 1, and continues to become infinitely closer to one, but does not actually equal one.

[darknessdweller]

At 4/28/08 04:07 PM, solardave wrote: I don't really care.

/second\

[Evark]

At 4/28/08 04:15 PM, Evark wrote: That part right there, in it's wrongness, is what makes your proof possible. 10x - x = 10.

/me facepalms. I'm an idiot. ORDER OF OPERATIONS.

9.9999999999 - .99999999999 does in fact, equal 9 even.

I still hate this proof. >: (

[MinusNick]

What a ground-breakingly new idea!!!!!! I prove it like this:
0.9~ Chuck Norris 1

Cock joke

[flubeca]

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~.

If you know any other proofs for 1 = 0.9~, please share them, or if you wish to challenge the validity of my proof or the statement that 1 = 0.9~, feel free to provide a critique.

so is x = 1 or = 0.9~

[CatherineElizabeth]

At 4/28/08 04:15 PM, Evark wrote:

At 4/28/08 04:06 PM, CatherineElizabeth wrote: 10x - x = 9.9~ - x
9x = 9

That part right there, in it's wrongness, is what makes your proof possible. 10x - x = 10.

Mind proving why that portion is wrong? It's completely legitimate Algebra.

If you know any other proofs for 1 = 0.9~, please share them, or if you wish to challenge the validity of my proof or the statement that 1 = 0.9~, feel free to provide a critique.

Regardless, I've seen proofs that do it without mistakes such as the above. I don't agree with them, they simply take advantage of the human inability to express the infinite to prove something stupid. .9~ approaches 1, and continues to become infinitely closer to one, but does not actually equal one.

The problem with your analysis here is that you equivocate the "jumping halfway and then halfway of that and halfway of that" (in this case, adding 0.9 and then 0.09 and then 0.009) where reaching the "goal" is impossible with a repeating decimal. In the former, you require a progressive geometric sequence, while in the latter nothing is being added, it just exists. Those who don't understand the infinite are the ones who make the mistake that 0.9~ does not equal 1.

[Fyndir]

Hello.

I am standing next to you.

Therefore I am you.

wait, what?

[CatherineElizabeth]

At 4/28/08 04:22 PM, Fyndir wrote: Hello.

I am standing next to you.

Therefore I am you.

wait, what?

Standing infinitely next to you, buddy.

[BonusStage]

At 4/28/08 04:15 PM, Evark wrote: That part right there, in it's wrongness, is what makes your proof possible. 10x - x = 10.

Nope, it equals 9x. Sorry Evan.

Also, he's doing the good answer and not being a fag trying to prove 0 = 1 or something since you can make 0 = anything by use of "math"

[Tsuchinoko]

At 4/28/08 04:15 PM, Evark wrote:

At 4/28/08 04:06 PM, CatherineElizabeth wrote: 10x - x = 9.9~ - x
9x = 9

That part right there, in it's wrongness, is what makes your proof possible. 10x - x = 10.

If you know any other proofs for 1 = 0.9~, please share them, or if you wish to challenge the validity of my proof or the statement that 1 = 0.9~, feel free to provide a critique.

Regardless, I've seen proofs that do it without mistakes such as the above. I don't agree with them, they simply take advantage of the human inability to express the infinite to prove something stupid. .9~ approaches 1, and continues to become infinitely closer to one, but does not actually equal one.

/topic

All you do is round .999999999999999999999999999999999999999 9999999999999999999999999999999999999999 9999999999999999999999999999999999999999 9999999999999999 to 1.

[mariomusicmaker1]

Yea, i never liked that.. my math teacher told the class that it is false but had little evidence to prove it,

[InsertFunnyUserName]

At 4/28/08 04:15 PM, Evark wrote: That part right there, in it's wrongness, is what makes your proof possible. 10x - x = 10.

10x - x = 10x - 1x.
10x - x = 9x.

[Tsuchinoko]

I don't think I can disprove everything there since I'm only in the 8th grade and I haven't been thought about imaginary numbers yet.

Now, you're saying that .9~ is a infinite number right? Doesn't that mean that it never ends? Therefor it can never equal one, but only be a approximation.

[subpar]

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~.

True, but the proof is idiotic, because you're practically using the assumption that 0.9~ = 1 to get to your answer. The only way that a number and ten times that number could possibly have a difference of 9 is if that number equals 1 to begin with. Simple algebra.

Besides, no one cares that 0.999... equals 1. It's just one of those silly facts that math professors use to confuse students, and there's no practical use for it, nor is there any reason to prove it unless you're too much of a douchebag to realize that any number with multiple consecutive nines after the decimal point should be rounded up anyway.

By the way, I can do stupid shit with numbers, too:

a = x
a+a = a+x
2a = a+x
2a-2x = a+x-2x
2(a-x) = a+x-2x
2(a-x) = a-x
Therefore, 2 = 1

Okay, so that's completely wrong. But you get the point.

[Zodomizer]

x=1
x/9=1/9
x/9=.1111111
x=.1111111(9)
x=.9999999

Dude, I just got that from nowhere! :U

[Fyndir]

At 4/28/08 04:23 PM, CatherineElizabeth wrote: Standing infinitely next to you, buddy.

Still wouldn't make you me.

[LampFace]

At 4/28/08 04:13 PM, CatherineElizabeth wrote:

Repeating. I can't make the repeating symbol normally used in Algebra (the bar over the number), so I use the next best thing, the tilda sign.

So 09.~ is 0.99999999999999999999999999999999999999 99999..... and all the way to infinity.

Actually it is a dot . not a bar and what about 9' that would do.

[Procrastination]

pi is excatly 3!

[CatherineElizabeth]

At 4/28/08 04:37 PM, subpar 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~.

True, but the proof is idiotic, because you're practically using the assumption that 0.9~ = 1 to get to your answer. The only way that a number and ten times that number could possibly have a difference of 9 is if that number equals 1 to begin with. Simple algebra.

No where have I assumed that 0.9~ = 1. To your second sentence, that's why 0.9~ equals 1, duh!

Besides, no one cares that 0.999... equals 1. It's just one of those silly facts that math professors use to confuse students, and there's no practical use for it, nor is there any reason to prove it unless you're too much of a douchebag to realize that any number with multiple consecutive nines after the decimal point should be rounded up anyway.

Tell me, what number comes in between 0.999~ and 1? There isn't one, so 0.999~ equals one because two different numbers have an infinite number of numbers between.

By the way, I can do stupid shit with numbers, too:

a = x
a+a = a+x
2a = a+x
2a-2x = a+x-2x
2(a-x) = a+x-2x
2(a-x) = a-x
Therefore, 2 = 1
Look at 2(a-x) =
Okay, so that's completely wrong. But you get the point.

I get the point, you can do stupid shit with numbers and make yourself look stupid. Good job.

[whthwthwtwhhhththwhh]

At 4/28/08 04:15 PM, Evark wrote: Regardless, I've seen proofs that do it without mistakes such as the above. I don't agree with them, they simply take advantage of the human inability to express the infinite to prove something stupid. .9~ approaches 1, and continues to become infinitely closer to one, but does not actually equal one.

Or perchance, maybe this arises from your inability to comprehend how the numbers react at infinity, you douche.

[CatherineElizabeth]

At 4/28/08 04:42 PM, Fyndir wrote:

At 4/28/08 04:23 PM, CatherineElizabeth wrote: Standing infinitely next to you, buddy.

Still wouldn't make you me.

No, but we would be in the same spot.