Off Topic: The Flood
This topic has moved here: Subject: Let's learn how to find the area of a rectangle!
  • Subject: Let's learn how to find the area of a rectangle!
Subject: Let's learn how to find the area of a rectangle!
  • gamertag: [none]
  • user homepage:

"Both optimists and pessimists contribute to our society. The optimist invents the airplane and the pessimist the parachute. " ~Gil Stern

"The difference between stupidity and genius is that genius has its limits." ~Albert Einstein

"What did I just drink?"~Socrates

Buyer's Guide: Headphones|Google Chrome Themes|Arena Spreadsheet

Posted by: Elite_Buddy
By using your brain and coming to a conclusion, you will always be a tiny fraction off one.

You know what, -blam!- it. You're being an ignorant bigot.


There is a mathematically sound proof that proves .9999 repeating equals 1...There isn't any need to be mad.

  • 12.10.2010 1:33 PM PDT

"Give me a place to stand, and I will move the Earth."
-Archimedes

Half-Life Universe
Secular Sevens
Posted by: Soviet Revival
the only thing philosophical about this thread is mister math.


Posted by: Elite_Buddy
By using your brain and coming to a conclusion, you will always be a tiny fraction off one.

You know what, -blam!- it. You're being an ignorant bigot.
You seem to be suggesting that there exists n = 10^-p, such that 1 - 0.999... = n. This is false, as shown in a number of analytic proofs. Would you like to see the proofs?

  • 12.10.2010 1:35 PM PDT

Posted by: drummer0702
Posted by: Elite_Buddy
By using your brain and coming to a conclusion, you will always be a tiny fraction off one.

You know what, -blam!- it. You're being an ignorant bigot.


There is a mathematically sound proof that proves .9999 repeating equals 1...There isn't any need to be mad.
There is proof that you are wrong! Where you ask? Your brain. Sure, there's mathimatic formualas that do this that blah blah blah, but that doesn't mean it equals 1.
0.99999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999 (I won't continue to save space) still doesn't equal one because we are still that tiny fraction off 1.

Yes, I would like to see proof. Then I shall resume my llama slumber.

[Edited on 12.10.2010 1:37 PM PST]

  • 12.10.2010 1:36 PM PDT
  •  | 
  • Fabled Legendary Member

They call me graland.

Posted by: Mister Math
Posted by: Elite_Buddy
Well, I'm presuming you're trying to write the doesn't equal sign, so yes. Because 0.9 recurring is not equal to 1. It's as close as you can get to 1 without getting to 1 though.
The set of reals (or rationals, for that matter) is dense, FYI. This means there is ALWAYS a number between any two numbers you can pick; therefore, there is no number that is as close to 1 as possible without being 1. If they are distinct numbers, there will be an infinite amount of numbers between them. Also, analytic proofs suggest that even if you could have 1 - w where w is infinitesimal, this number still would not be represented by 0.999..., and 0.999... would still equal 1.

Does that mean that 1.999 = 2? Does 2.999 = 3, ad infinitum?

  • 12.10.2010 1:37 PM PDT
  • gamertag: [none]
  • user homepage:

"Both optimists and pessimists contribute to our society. The optimist invents the airplane and the pessimist the parachute. " ~Gil Stern

"The difference between stupidity and genius is that genius has its limits." ~Albert Einstein

"What did I just drink?"~Socrates

Buyer's Guide: Headphones|Google Chrome Themes|Arena Spreadsheet

Posted by: Elite_Buddy
(I won't continue to save space) still doesn't equal one because we are still that tiny fraction off 1.


What's that fraction then?

  • 12.10.2010 1:37 PM PDT

"Give me a place to stand, and I will move the Earth."
-Archimedes

Half-Life Universe
Secular Sevens
Posted by: Soviet Revival
the only thing philosophical about this thread is mister math.


Posted by: Elite_Buddy
. . . still doesn't equal one because we are still that tiny fraction off 1.
What is this fraction? I'll make it easier for you:

1 - 0.999... = 1/(10^p)

What is p?
Posted by: Garland
Posted by: Mister Math
Posted by: Elite_Buddy
Well, I'm presuming you're trying to write the doesn't equal sign, so yes. Because 0.9 recurring is not equal to 1. It's as close as you can get to 1 without getting to 1 though.
The set of reals (or rationals, for that matter) is dense, FYI. This means there is ALWAYS a number between any two numbers you can pick; therefore, there is no number that is as close to 1 as possible without being 1. If they are distinct numbers, there will be an infinite amount of numbers between them. Also, analytic proofs suggest that even if you could have 1 - w where w is infinitesimal, this number still would not be represented by 0.999..., and 0.999... would still equal 1.

Does that mean that 1.999 = 2? Does 2.999 = 3, ad infinitum?
Let's check:

0.999... = 1
Add 1
1.999... = 2
Add 1
2.999... = 3

Seems to work out, so yes.

And yes, 0.4999... = 0.5.

[Edited on 12.10.2010 1:39 PM PST]

  • 12.10.2010 1:37 PM PDT

Posted by: drummer0702
Posted by: Elite_Buddy
(I won't continue to save space) still doesn't equal one because we are still that tiny fraction off 1.


What's that fraction then?
-_- I hate you. :D

The fraction is impossible to comprehend. It's like infinity, or the concept of nothing.

[Edited on 12.10.2010 1:38 PM PST]

  • 12.10.2010 1:37 PM PDT

"Give me a place to stand, and I will move the Earth."
-Archimedes

Half-Life Universe
Secular Sevens
Posted by: Soviet Revival
the only thing philosophical about this thread is mister math.


Posted by: Elite_Buddy
Posted by: drummer0702
Posted by: Elite_Buddy
(I won't continue to save space) still doesn't equal one because we are still that tiny fraction off 1.


What's that fraction then?
-_- I hate you. :D

The fraction is impossible to comprehend. It's like infinity, or the concept of nothing.
Not impossible to comprehend. Millions of mathematicians do.

Now don't dodge the question, answer. Feel free to use limits if you want.

[Edited on 12.10.2010 1:40 PM PST]

  • 12.10.2010 1:39 PM PDT
  • gamertag: [none]
  • user homepage:

"Both optimists and pessimists contribute to our society. The optimist invents the airplane and the pessimist the parachute. " ~Gil Stern

"The difference between stupidity and genius is that genius has its limits." ~Albert Einstein

"What did I just drink?"~Socrates

Buyer's Guide: Headphones|Google Chrome Themes|Arena Spreadsheet

Posted by: Elite_Buddy
-_- I hate you. :D

The fraction is impossible to comprehend. It's like infinity, or the concept of nothing.


;)

  • 12.10.2010 1:40 PM PDT

THREEEEEEEEEEEEEEEEE POINT. ONE. FOUR. ONE. FIVE. NINE. TWO. SIX. FIVE. THREE. FIVE. EIGHT. TWO. SEVEN. NINE...
Jesus.
I don't know the rest.

Posted by: Real Madrid
Guys, let's find the exact value of PI!

-RM-

  • 12.10.2010 1:41 PM PDT


Posted by: Mister Math

Posted by: Elite_Buddy
Posted by: drummer0702
Posted by: Elite_Buddy
(I won't continue to save space) still doesn't equal one because we are still that tiny fraction off 1.


What's that fraction then?
-_- I hate you. :D

The fraction is impossible to comprehend. It's like infinity, or the concept of nothing.
Not impossible to comprehend. Millions of mathematicians do.

Feel free to use limits if you want.
Well, it's not possible to believe, to see, you probably know what I mean. Try and imagine the universe before the big bang. That sorta thing.

  • 12.10.2010 1:41 PM PDT

Posted by: Elite_Buddy
Posted by: drummer0702
Posted by: Elite_Buddy
(I won't continue to save space) still doesn't equal one because we are still that tiny fraction off 1.


What's that fraction then?
-_- I hate you. :D

The fraction is impossible to comprehend. It's like infinity, or the concept of nothing.
Disregarding the question by stating that the fraction is a conundrum. Nice.

  • 12.10.2010 1:41 PM PDT
  •  | 
  • Fabled Legendary Member

They call me graland.


Posted by: Mister Math
Let's check:

0.999... = 1
Add 1
1.999... = 2
Add 1
2.999... = 3

Seems to work out, so yes.

And yes, 0.4999... = 0.5.

The reason I asked is because all I ever hear about is 0.999 = 1; I've never heard anyone mention anything above that (or if it could even be applied to any other numbers).

  • 12.10.2010 1:42 PM PDT
  • gamertag: [none]
  • user homepage:

Never give up on your dreams... unless you wanna be an astronaut.

-Krispy Kreme

Reading this made me feel like an idiot.

  • 12.10.2010 1:42 PM PDT
  •  | 
  • Fabled Legendary Member

Posted by: Elite_Buddy
Well, it's not possible to believe, to see, you probably know what I mean. Try and imagine the universe before the big bang. That sorta thing.

Done.

Next.

  • 12.10.2010 1:43 PM PDT


Posted by: Lies
Posted by: Elite_Buddy
Well, it's not possible to believe, to see, you probably know what I mean. Try and imagine the universe before the big bang. That sorta thing.

Done.

Next.
Explain what you saw.

  • 12.10.2010 1:44 PM PDT

"Give me a place to stand, and I will move the Earth."
-Archimedes

Half-Life Universe
Secular Sevens
Posted by: Soviet Revival
the only thing philosophical about this thread is mister math.


Posted by: Elite_Buddy
Well, it's not possible to believe, to see, you probably know what I mean. Try and imagine the universe before the big bang. That sorta thing.
You have no idea what the 0.999... = 1 theorem has to do with, do you? It's okay, it'd be silly to think lesser of someone for not knowing calculus. I'll give the analytic proofs.

http://www.wolframalpha.com/input/?i=lim+%28x+to+infinity%29+ %2810^x+-+1%29+%2F+%2810^x%29

http://www.wolframalpha.com/input/?i=9+*+%28sum%28k+%3D+1%2C+ infinity%29+1%2F%2810^k%29%29

http://www.wolframalpha.com/input/?i=lim+%28x+to+infinity%29+ 1%2F%2810^x%29
Posted by: Garland

Posted by: Mister Math
Let's check:

0.999... = 1
Add 1
1.999... = 2
Add 1
2.999... = 3

Seems to work out, so yes.

And yes, 0.4999... = 0.5.

The reason I asked is because all I ever hear about is 0.999 = 1; I've never heard anyone mention anything above that (or if it could even be applied to any other numbers).
Well, not any other number. You can't do that with repeating decimals or irrationals, because they have no ultimate digit.

[Edited on 12.10.2010 1:47 PM PST]

  • 12.10.2010 1:45 PM PDT

"Find where the liar hides, so that I may place my boot between his gums!" - Rtas 'Vadum

Posted by: Disambiguation
First, let's consider a rectangle. On a coordinate plane, we'll say it has vertices at (0,0), (a,0), (0,b), and (a,b)

Mm'kay.

Posted by: Disambiguation
Then, an orthogonal parametrization of the boundary can be obtained by taking F(x,y) = (ax, by)

Parametrization?

Posted by: Disambiguation
The domain of F is D = {(x,y): 0 <= x <= 1, 0 <= y <= 1}

Okay...ish. Not exactly sure why the domain is that, probably because I do not understand the last part.

Posted by: Disambiguation
Our general formula claims that: Area = integral (sqrt [[ Fx*Fx, Fx*Fy][Fy*Fx, Fy*Fy]] over the domain D.

O_o

Posted by: Disambiguation
The * operation in this case is the vector scalar product. Since the matrix is positive definite, the root of its determinant will never be imaginary so we will always have a positive or zero real area.

Positive definite, blargh.

Posted by: Disambiguation
The partial derivatives can be easily computed to be
Fx = (a, 0) and Fy = (0, b)

Evaluating the determinant yields a^2*b^2, so that sqrt(a^2*b^2) = a*b

Integrating over [0,1] with respect to x and over [0,1] with respect to y yields Area = (a*b)*1*1 = a*b

I guess the last bits forbid me from grasping this bit.

Posted by: Disambiguation
So, everyone except Anton can see that the area of a rectangle is, perhaps not obviously, the product of the lengths of its sides.

Fix'd. ;)

  • 12.10.2010 1:46 PM PDT
  •  | 
  • Fabled Legendary Member

Posted by: Elite_Buddy

Posted by: Lies
Posted by: Elite_Buddy
Well, it's not possible to believe, to see, you probably know what I mean. Try and imagine the universe before the big bang. That sorta thing.

Done.

Next.
Explain what you saw.

What I saw transcends spoken language. Lol I was kidding, but for real that's a pointless exercise:

"Asked in October 2005 on the British daytime chat show Richard & Judy, to explain his assertion that the question "What came before the Big Bang?" was meaningless, he [Stephen Hawking] compared it to asking "What lies north of the North Pole?"

  • 12.10.2010 1:47 PM PDT

Posted by: Lies
Posted by: Elite_Buddy

Posted by: Lies
Posted by: Elite_Buddy
Well, it's not possible to believe, to see, you probably know what I mean. Try and imagine the universe before the big bang. That sorta thing.

Done.

Next.
Explain what you saw.

What I saw transcends spoken language. Lol I was kidding, but for real that's a pointless exercise:

"Asked in October 2005 on the British daytime chat show Richard & Judy, to explain his assertion that the question "What came before the Big Bang?" was meaningless, he [Stephen Hawking] compared it to asking "What lies north of the North Pole?"
That's my point. You can't actually imgaine, see ect the actual fraction. It never ends, it's always getting smaller. Now, in case I don't see ya, good morning, good evening and good night. Zzzzz

[Edited on 12.10.2010 1:49 PM PST]

  • 12.10.2010 1:49 PM PDT

"Give me a place to stand, and I will move the Earth."
-Archimedes

Half-Life Universe
Secular Sevens
Posted by: Soviet Revival
the only thing philosophical about this thread is mister math.


Posted by: Elite_Buddy
That's my point. You can't actually imgaine, see ect the actual fraction. It never ends, it's always getting smaller. Now, in case I don't see ya, good morning, good evening and good night. Zzzzz
It's not getting smaller, it's not doing snything. If you want to think of it as a limit, it'd be 0; as in, the difference between 0.999... and 1 are 0.

  • 12.10.2010 1:50 PM PDT

"The individual has always had to struggle to keep from being overwhelmed by the tribe. If you try it, you will be lonely often, and sometimes frightened. But no price is too high to pay for the privilege of owning yourself."
-Nietzsche

There's a simple algebraic proof. Some people like to argue with it, although I can assure you it's as rigorous as all of the ones using calculus. Here it is:

Let x = 0.999 . . . repeating ad infinitum

Multiply both sides by 10
-> 10x = 9.999 . . .

Subtract 9 from both sides
-> 10x - 9 = 0.999 . . .

But wait! 0.999 . . . = x
-> 10x - 9 = x

Adding 9 to both sides
-> 10x = x + 9

Subtracting x from both sides
-> 9x = 9

Dividing by 9
-> x = 1

Therefore, 0.999 . . . equals 1.

QED.

Edit: I'm off to class. Thanks for using my thread to discuss mathematics! Feel free to continue this discussion, don't let it die! Math is important.

[Edited on 12.10.2010 1:59 PM PST]

  • 12.10.2010 1:57 PM PDT

"Give me a place to stand, and I will move the Earth."
-Archimedes

Half-Life Universe
Secular Sevens
Posted by: Soviet Revival
the only thing philosophical about this thread is mister math.


Posted by: Disambiguation
Feel free to continue this discussion, don't let it die! Math is important.
Indeed. Anyone else have any misconceptions about 0.999... = 1?

  • 12.10.2010 2:09 PM PDT

Good old hypocrisy, what humanity does best.

Well looks like I need to learn some more maths.

Is this vector calculus? Also why did you introduce determinants? What do matrices have to do with this?

  • 12.10.2010 2:13 PM PDT

____________(˜˜˜||˜˜˜˜||˜˜˜˜˜)_∏______
l ---------____.`=====.-.~:________\___|================[oo]
|_|||___/___/_/~```|_|_|_|``(o)----------<)

Im Russian, deal with it.
Im not responsible for what you do with my advice.


Posted by: Mister Math

Posted by: Disambiguation
Feel free to continue this discussion, don't let it die! Math is important.
Indeed. Anyone else have any misconceptions about 0.999... = 1?

.999999999... <1

And 1.00000(insert almost infinate zeros)0001>1

  • 12.10.2010 2:13 PM PDT