Math proof that 2 = 1

[Krynn72]

But im not. Im thinking of it never ending. It will never reach a point where its the same as 1. The 9s go on forever and ever, so it always falls short of 1.

That statement you quoted is what I think is incorrect. If you stop it at 0.999...999 then logic would conclude that it isnt 1 (which contradicts that statement that says we would conclude it is 1), because it ended as 0.999...999.

 

[Cole]

But im not. Im thinking of it never ending. It will never reach a point where its the same as 1. The 9s go on forever and ever, so it always falls short of 1.

It does not fall short of one. Because the nines go on forever. You can't think of the nines as stopping, and if they never stop then they can never fall short. You can't think of it as just add a 9, nope fall shorts... lets add another 9.. and repeat. You have to think of it as infinite 9's that never stop, not adding 9's forever.

1 and .9... is in fact the same number, just different symbols.

I mean there are basic proofs such as:
1/3 = 0.333...
3(1/3) = 3*0.333...
1 = 0.999...

and

(You can use this to find fractions.)
x = .999...
10x = 9.999...
10x - x = 9.999... - .999...
9x = 9
x = 1
Therefor the fraction equvilant of .999... is 1/1

Whats the fraction equivlant of .333...?
x = .333...
10x = 3.333...
10 x - x = 3.333... - .333...
9x = 3
x = 3/9 = 1/3

http://en.wikipedia.org/wiki/0.999...

 

[CyberPitz]

You can't really think of it that way.

"you're _really_ thinking of

0.999...999

which is not the same thing. You're absolutely right that 0.999...999
is a little below 1, but 0.999999... doesn't fall short of 1 _until_
you stop expanding it. But you never stop expanding it, so it never falls short of 1."

See? It HAS to be 1.

It will always be infinately smaller than EVERY number, so because it is infinatly smaller than one number, makes it the same? That's like saying a square that has been cut .999... Millimeters short, which techinically makes it a rectangle, but hell, it's infinately close to the square, it's the same.

I probably explained that retarded like, but that's the best explanation I can think of here at work.

 

[Krynn72]

It does not fall short of one. Because the nines go on forever. You can't think of the nines as stopping, and if they never stop then they can never fall short. You can't think of it as just add a 9, nope fall shorts... lets add another 9.. and repeat. You have to think of it as infinite 9's that never stop, not adding 9's forever.

1 and .9... is in fact the same number, just different symbols.

http://en.wikipedia.org/wiki/0.999...

I understand the math, and I see that it works... but I guess its one of those thing that I will never understand the concept of. It just seems to have no sort of logic behind it. I suppose my problem is that I think about things in a more philosophical way and try to understand the idea before being able to prove it.

I wont disagree with it, because it seems to have been proven, but its something I will never understand.

 

[Dan]

Here's a physics question for you:

A 65 lb refridgerator is sitting on top of 3 springs with stiffness k [lb/in] each. If the fridge motor runs at 580 rpm what should be the value of the spring stiffness k such that only 10% of the shaking force of the fridge is transmitted to the floor. You can ignore viscous damping.

 

[Stigmata]

Keep your homework to yourself, Dan

 

[TCfromBN]

The part where you can tell it doesn't equal one is where it says 0.xxxxxxxxx.....

Also, there are infinite decimal places to fill, so you can never reach a point to make the number equal to one. You can make it as many decimal places as you want. However, if your going to make it infinite, to measure the distance from 1 back to .999... your going to have to go infinite decimal places to describe it.

This is just like 9/10 99/100 999/1000 9999/10000 ... etc, you never get to a point where the numerator has more numbers than the denominator, because you have to add a number on both the top and bottom. There will be infinite numbers in the numerator and denominator, except the denominator will have infinite+1 numbers.

 

[Asus]

I dont think .99... equals 1 but i think it approximates 1.
You can't use .33... = 1/3 to prove it because it's the same thing in question.

 

[Solaris]

I dont think .99... equals 1 but i think it approximates 1.
You can't use .33... = 1/3 to prove it because it's the same thing in question.

Now this is why I love maths. With maths, if something is proved mathematically, built on sound axioms, and the proof has no faults. Then whatever is proven is true, with 100% certainty and always will be. If you [Asus] don't agree with the assumption that 0.333..=1/3 try and do it on paper, you will find the 3's will keep coming till infinity. By disagreeing with 0.333=1/3 you disagreeing with the most basic of mathematical axioms, which ironically cannot be proven.

 

[Krynn72]

I just found difinitive proof that 0.999... does not equal 1. Will post in a sec.

 

[Solaris]

I just found difinitive proof that 0.999... does not equal 1. Will post in a sec.

No you didn't. I want it in mathematical format. In maths we don't write essays.

 

[Krynn72]

Ok, here is my definitive proof. There is no possible way you can deny this, I have thought it over, and everyone I know agrees that its flawless.


.
.
.
.

I asked an online magic 8 ball:

 

[Asus]

Now this is why I love maths. With maths, if something is proved mathematically, built on sound axioms, and the proof has no faults. Then whatever is proven is true, with 100% certainty and always will be. If you [Asus] don't agree with the assumption that 0.333..=1/3 try and do it on paper, you will find the 3's will keep coming till infinity. By disagreeing with 0.333=1/3 you disagreeing with the most basic of mathematical axioms, which ironically cannot be proven.

I didn't say 1/3 != .33(3) but i did loose my train of thought on my point. lol

 

[Stigmata]

I dont think .99... equals 1 but i think it approximates 1.
You can't use .33... = 1/3 to prove it because it's the same thing in question.

Well my point is that 0.333... and 0.999... are representations of real numbers - 1/3 and 1, respectively.

 

[Remus]

Ok, here is my definitive proof. There is no possible way you can deny this, I have thought it over, and everyone I know agrees that its flawless.


I asked an online magic 8 ball

Well... I can't argue with that:E

Also on a side note: In Soviet Russia, eight ball you!

 

[ktimekiller]

Lets just agree, it works in theory, but its just not logically possible yea?

 

[Stigmata]

It's logically possible, but many people don't properly understand the concept of an infinite series, and thus can't "logically" accept that 0.999... equals 1.

 

[<RJMC>]

to hell whit you math freaks

calculate how many bullets I put in your brains

*me pulls out machinegun and shoot everyone*

 

[Cole]

RJMC, never come to my school.

 

[Reginald]

to hell whit you math freaks

calculate how many bullets I put in your brains

*me pulls out machinegun and shoot everyone*

Hahahahaha.

<3

Do we get 0.9999... bullets each?

 

[Geogaddi]

Three men stay at a hotel for the night. The innkeeper charges thirty dollars per room per night. The men rent one room; each pays ten dollars. The bellhop leads the men to their room. Later, the innkeeper discovers he has overcharged the men and asks the bellhop to return five dollars to them. On the way upstairs, the bellhop realizes that five dollars can't be evenly split among three men, so he decides to keep two dollars for himself and return one dollar to each man.

At this point, the men have paid nine dollars each, totalling 27. The bellhop has two, which adds up to 29. Where did the thirtieth dollar go?

 

[Que-Ever]

Check your anus.

 

[Reginald]

Three men stay at a hotel for the night. The innkeeper charges thirty dollars per room per night. The men rent one room; each pays ten dollars. The bellhop leads the men to their room. Later, the innkeeper discovers he has overcharged the men and asks the bellhop to return five dollars to them. On the way upstairs, the bellhop realizes that five dollars can't be evenly split among three men, so he decides to keep two dollars for himself and return one dollar to each man.

At this point, the men have paid nine dollars each, totalling 27. The bellhop has two, which adds up to 29. Where did the thirtieth dollar go?

The innkeeper has 25, the bellhop has 2 and the men have 1 dollar each totaling 3.

25 + 2 + 3 = 30.

I don't see the problem.

 

[Baal]

I didn't say 1/3 != .33(3) but i did loose my train of thought on my point. lol

I think you got intimidated by him, don't back down, you know what you meant.

At least, from what I got out of you, was that saying 0.3333... = 1/3 and therefore 0.9999... = 1 is a poor way of describing the issue at hand because it's the same issue on both ends of the problem. And if someone can't comprehend 0.9999... = 1 then they can't comprehend 0.3333 = 1/3, or at least 0.3333... * 3 = 1

 

[CyberPitz]

The innkeeper has 25, the bellhop has 2 and the men have 1 dollar each totaling 3.

25 + 2 + 3 = 30.

I don't see the problem.

When I read the story, I get 29, when I do the math on paper, I get 30

****!

 

[Reginald]

When I read the story, I get 29, when I do the math on paper, I get 30

****!

I've always had a mind that works things like that out quite easily. I mean, it's obvious to me you can't count what people have with what people spent... if that makes sense. It's all in the way the question is worded.

 

[Krynn72]

The innkeeper has 25, the bellhop has 2 and the men have 1 dollar each totaling 3.

25 + 2 + 3 = 30.

I don't see the problem.

You didnt answer the question though. You worded it differently to get around the question. If you look at it the way the question was asked, it looks like a dollar is missing, its your job to explain where it went!

 

[Reginald]

You didnt answer the question though. You worded it differently to get around the question. If you look at it the way the question was asked, it looks like a dollar is missing, its your job to explain where it went!

That is where it went. There is no way to SOLVE this. There is no MISSING dollar. It is just a case of wording it differently.

OK then, the men paid 9 quid each, but the 2 quid of the bellhop is part of that 27. It's the 3 that is left over, not the two.

 

[Qonfused]

Three men stay at a hotel for the night. The innkeeper charges thirty dollars per room per night. The men rent one room; each pays ten dollars. The bellhop leads the men to their room. Later, the innkeeper discovers he has overcharged the men and asks the bellhop to return five dollars to them. On the way upstairs, the bellhop realizes that five dollars can't be evenly split among three men, so he decides to keep two dollars for himself and return one dollar to each man.

At this point, the men have paid nine dollars each, totalling 27. The bellhop has two, which adds up to 29. Where did the thirtieth dollar go?

They had buttsex. That's all I care about.

 

[Krynn72]

That is where it went. There is no way to SOLVE this. There is no MISSING dollar. It is just a case of wording it differently.

OK then, the men paid 9 quid each, but the 2 quid of the bellhop is part of that 27. It's the 3 that is left over, not the two.

??? I didnt follow that last line.


But the answer to his question is:

"Its a trick question"

 

[ktimekiller]

if you go through it, it adds to 30, but if you go through 9x3, and 2 to bellhop, it adds to 29 lol.

 

[Reginald]

if you go through it, it adds to 30, but if you go through 9x3, and 2 to bellhop, it adds to 29 lol.

But if they each paid 9, thats 25 to the manager and 2 to the bellhop. MAking 27. Then they each have a quid making thirty.

I never understood why people got confused about it. It's only because it plants an idea in your head that you become confused.

 

[Cole]

Three men stay at a hotel for the night. The innkeeper charges thirty dollars per room per night. The men rent one room; each pays ten dollars. The bellhop leads the men to their room. Later, the innkeeper discovers he has overcharged the men and asks the bellhop to return five dollars to them. On the way upstairs, the bellhop realizes that five dollars can't be evenly split among three men, so he decides to keep two dollars for himself and return one dollar to each man.

At this point, the men have paid nine dollars each, totalling 27. The bellhop has two, which adds up to 29. Where did the thirtieth dollar go?

They men payed $35(5 dollors over).
So the bellhop goes to bring up 5 ones.
He keeps 2 ones.
1 one goes to each men.

There is no dollor missing.

Although somethings wrong. The men payed $30. A single room costs $30. The innkeeper did not overcharge them, yet the story says they did. Therefor, there is no dollor missing. (According to the proofs you do a Geometry class).

It could be assumed the the Innkeeper is wrong about overcharging them which seems to be the case. Each man ended up paying $9. The men payed $27. The bellhop has $2. However, in actuality where did that dollar go?
The bellhop could have it, the men could have it, or it could be in the register. Because the men payed that money. However, when the bellhop grabbed $5, it could have been in that. The bellhop, could have also given it to the men. However this is still technically getting away from the question.

The story is faulty, the question is bad question. That simple. It wants to know where the missing dollor is. However the information it is using to realize that there is a missing dollar is slanted. If the information is slanted, the question is stupid, and stupid questions are retarded and therefor do not need to be answered.

Simply, the information given from the question is bad. It's like saying, 1 + x = 2 where x = 3. Obviously the information about x is wrong.

 

[MiccyNarc]

The two is part of the 27, the men each have 3, = 30, there is no missing dollar, no matter how you look at it.

 

[Cole]

The two is part of the 27, the men each have 3, = 30, there is no missing dollar, no matter how you look at it.

You got that wrong.
The 27 comes from how much money the men spent.
The two comes from how much money the kid has.

The problem is, there adding data that you can't add. I mean adding the 27 and 2 would be no different than me saying:
The men payed $30 initially, the boy has $2. thats $32. Where did the extra $2 come from?

Not only that but the story is faulty.

 

[Tollbooth Willie]

Oh shi-

You don't think he's figured out about the....

Oh God. Call the president.