<!--QuoteBegin-raz0r+Mar 22 2005, 08:42 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (raz0r @ Mar 22 2005, 08:42 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> if e^i(pi) is imaginary, then how can it = 0? If a number is imaginary, it does not exist, and there is no way to write it down on paper, so therefore it cannot equal 0. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> wrong. It can have a 0 real component.
Sheesh, and here I was thinking that I would actually fool someone. Yes I know that the proof doesn't work. This line in particular: <!--QuoteBegin--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> </td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->e^i(pi) is imaginary, a zero in the realm of real numbers<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd--> is a travesty of mathematics. I've pulled this same stunt at my school, and people believed me, so congrats, you're all smarter than the average high schooler. <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo-->
@Whee: Yes it can have a zero component, but since it's not specified it's hardly something you can base a proof on.
<!--QuoteBegin-Rob+Mar 22 2005, 05:46 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (Rob @ Mar 22 2005, 05:46 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> I prefer my High School math teacher's "proof" of the .999_ = 1 thing:
By definition, two numbers are the same IFF there exist no other numbers between them. I.E. 1 < x < 1 means x = 1, because there is no number between 1 and 1 except for 1.
So...
if .999_ goes on for infinity down the line, give me a number between .999_ and 1 that isn't one. BUT STRANGE THINGS HAPPEN AT INFINITY!!! Of course they do, that's why we use such an abstract concept of amounts of digits so big we can't understand them.
Just think of this: Euclide, the Father of Modern Geometry , expressed that he could not imagine a number of anything less than zero. He said, it's pointless to conceive of -1 * an integer.
Now, while we mostly agree that imaginary numbers are quite useful, how many of use can say we can understand what sqrt(-1) is? Maybe 1500 years from now it'll be obvious!
What I'm tryin to say is that it's whacked to think you can "prove" anything in any case. Math pros and Logic buffs throw these things around like it's some kinda power of God they weild. It's PROVEN that you can't do this, or that this always works. And it's true, as far as we're concerned today, but whose to say we have the whole picture anyway? <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> First man to get it right yet <!--emo&:)--><img src='http://www.unknownworlds.com/forums/html/emoticons/smile-fix.gif' border='0' style='vertical-align:middle' alt='smile-fix.gif' /><!--endemo-->
*hands Rob a well deserved beer*
Ya see... numbers mean jack all without something to represent them... thus a mathmatical equation CANNOT DISPROVE OR PROVE something... it can only STRENGTHEN the proof.
<!--QuoteBegin-Wheeee+Mar 22 2005, 10:32 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (Wheeee @ Mar 22 2005, 10:32 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> that's not necessarily true anyway. there are lots of mathematical proofs that have real-life implications that were proved using imaginary analysis. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> Yes, but how are we sure that what we're doing is actually right and not just coincidentally leading to a finite set of truths that fail near the boundries of that set?
The point is, we don't, and we never will. At least until someone proves that what we know does break down.
The forward movement of science has always been, and will always be, the proof of wrong. Someone proposes a new theory (and to this date, there are but a handful of actual mathematical "laws." Everything else is theory), which is accepted as absolute fact until someone can show a case where it doesn't work. Then it's back to the drawing board.
It's pretty much like everything in life. To build strength you exploit weakness and learn out to adapt. What irks me is how all these intellectuals beat their chests and say what brave men have conquered nature and how our civilization is truly the finest of all of God's creations.
Eh. That's question-begging. How do we know anything at all? As for the second part of your statement, mathematics is just a tool. It's possible to prove that we've been using it badly or wrongly, but it's not really possible to prove that it's in and of itself "wrong" when we already define it as "right" and it's logically consistent,
<!--QuoteBegin-Wheeee+Mar 22 2005, 11:55 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (Wheeee @ Mar 22 2005, 11:55 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> Eh. That's question-begging. How do we know anything at all? As for the second part of your statement, mathematics is just a tool. It's possible to prove that we've been using it badly or wrongly, but it's not really possible to prove that it's in and of itself "wrong" when we already define it as "right" and it's logically consistent, <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd--> You're right, we don't know anything at all. But that's not really a reason to despair. I'm just saying I dislike attitudes that forcefully assert that we DO know exactly what is what and how it works. This is simply ridiculus.
And about the last part of your statement. We may not think it's possible to prove wrong what we have defined as right, but I'm sure scholars in the days of Athens also thought it was impossible to prove that a negative number existed, because they defined thruth as being positive numbers only.
Time and time again, we are blinded by our own assumptions, and that doesn't mean that even if we realize it we can change it. I'm as much of a victim as anyone. Again, what I'm saying is that I disapprove of arrogant behavior, especially in matters of science and mathematics.
Seriously though... we can "prove" that we exist cause, duh, we're walkin round living, breathin, eatin, sleepin... but how do we know we're not a dream... how do we know we are not dreaming? Ever had that dream that you wake up, get cleaned up, dressed, and head out the door to the school bus... only to wake up? I've had that repeat three or four times before... let me tell you, you NEVER know which is the real deal 0o'
<!--QuoteBegin-BulletHead+Mar 23 2005, 01:10 AM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (BulletHead @ Mar 23 2005, 01:10 AM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> let me tell you, you NEVER know which is the real deal 0o' <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> Sure you do. At least I do. If I'm dreaming and ask myself "Am I dreaming?" the answer is always either "Yes" or "I don't know". When I'm awake and ask myself "Am I dreaming?" the answer is always "no".
<!--QuoteBegin-Wheeee+Mar 23 2005, 02:20 AM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (Wheeee @ Mar 23 2005, 02:20 AM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> just to be an ****, what if you're daydreaming?
<!--QuoteBegin-Wheeee+Mar 22 2005, 08:51 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (Wheeee @ Mar 22 2005, 08:51 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> 0.999_^2 > 0.999_8.... != 0.999_, therefore 0.999_ != 1 <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd--> That is a very silly assumption. Of course you already cover that with the words "disregarding the fact".
0.999_^2 = 0.999_
Yes, I'm possibly just being master of the obvious. I'm apologizing before hand just in case, Wheee.
both of the proofs i wrote are bogus <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo-->
Comments
If a number is imaginary, it does not exist, and there is no way to write it down on paper, so therefore it cannot equal 0. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
wrong. It can have a 0 real component.
<!--QuoteBegin--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> </td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->e^i(pi) is imaginary, a zero in the realm of real numbers<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
is a travesty of mathematics. I've pulled this same stunt at my school, and people believed me, so congrats, you're all smarter than the average high schooler. <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo-->
@Whee: Yes it can have a zero component, but since it's not specified it's hardly something you can base a proof on.
By definition, two numbers are the same IFF there exist no other numbers between them. I.E. 1 < x < 1 means x = 1, because there is no number between 1 and 1 except for 1.
So...
if .999_ goes on for infinity down the line, give me a number between .999_ and 1 that isn't one. BUT STRANGE THINGS HAPPEN AT INFINITY!!! Of course they do, that's why we use such an abstract concept of amounts of digits so big we can't understand them.
Just think of this: Euclide, the Father of Modern Geometry , expressed that he could not imagine a number of anything less than zero. He said, it's pointless to conceive of -1 * an integer.
Now, while we mostly agree that imaginary numbers are quite useful, how many of use can say we can understand what sqrt(-1) is? Maybe 1500 years from now it'll be obvious!
What I'm tryin to say is that it's whacked to think you can "prove" anything in any case. Math pros and Logic buffs throw these things around like it's some kinda power of God they weild. It's PROVEN that you can't do this, or that this always works. And it's true, as far as we're concerned today, but whose to say we have the whole picture anyway? <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
First man to get it right yet <!--emo&:)--><img src='http://www.unknownworlds.com/forums/html/emoticons/smile-fix.gif' border='0' style='vertical-align:middle' alt='smile-fix.gif' /><!--endemo-->
*hands Rob a well deserved beer*
Ya see... numbers mean jack all without something to represent them... thus a mathmatical equation CANNOT DISPROVE OR PROVE something... it can only STRENGTHEN the proof.
<!--emo&:p--><img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo-->
Yes, but how are we sure that what we're doing is actually right and not just coincidentally leading to a finite set of truths that fail near the boundries of that set?
The point is, we don't, and we never will. At least until someone proves that what we know does break down.
The forward movement of science has always been, and will always be, the proof of wrong. Someone proposes a new theory (and to this date, there are but a handful of actual mathematical "laws." Everything else is theory), which is accepted as absolute fact until someone can show a case where it doesn't work. Then it's back to the drawing board.
It's pretty much like everything in life. To build strength you exploit weakness and learn out to adapt. What irks me is how all these intellectuals beat their chests and say what brave men have conquered nature and how our civilization is truly the finest of all of God's creations.
You're right, we don't know anything at all. But that's not really a reason to despair. I'm just saying I dislike attitudes that forcefully assert that we DO know exactly what is what and how it works. This is simply ridiculus.
And about the last part of your statement. We may not think it's possible to prove wrong what we have defined as right, but I'm sure scholars in the days of Athens also thought it was impossible to prove that a negative number existed, because they defined thruth as being positive numbers only.
Time and time again, we are blinded by our own assumptions, and that doesn't mean that even if we realize it we can change it. I'm as much of a victim as anyone. Again, what I'm saying is that I disapprove of arrogant behavior, especially in matters of science and mathematics.
The Matrix has us All
>_>
<_<
>_>
*eats both red and blue pills*
*head pops off*
Seriously though... we can "prove" that we exist cause, duh, we're walkin round living, breathin, eatin, sleepin... but how do we know we're not a dream... how do we know we are not dreaming? Ever had that dream that you wake up, get cleaned up, dressed, and head out the door to the school bus... only to wake up? I've had that repeat three or four times before... let me tell you, you NEVER know which is the real deal 0o'
Sure you do. At least I do. If I'm dreaming and ask myself "Am I dreaming?" the answer is always either "Yes" or "I don't know". When I'm awake and ask myself "Am I dreaming?" the answer is always "no".
<!--emo&:D--><img src='http://www.unknownworlds.com/forums/html/emoticons/biggrin-fix.gif' border='0' style='vertical-align:middle' alt='biggrin-fix.gif' /><!--endemo-->
<!--emo&:D--><img src='http://www.unknownworlds.com/forums/html/emoticons/biggrin-fix.gif' border='0' style='vertical-align:middle' alt='biggrin-fix.gif' /><!--endemo--> <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
I don't daydream.
Look.
Definitions:
Women = time * money
Time = money
--> women = money * money
women = money²
money = the root of all evil
--> women = sqrt(evil²)
women = evil
q.e.d. <!--emo&;)--><img src='http://www.unknownworlds.com/forums/html/emoticons/wink-fix.gif' border='0' style='vertical-align:middle' alt='wink-fix.gif' /><!--endemo-->
P.S.: No offense meant! I love all women! Two of them particularly, including my mother.
<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
That is a very silly assumption. Of course you already cover that with the words "disregarding the fact".
0.999_^2 = 0.999_
Yes, I'm possibly just being master of the obvious. I'm apologizing before hand just in case, Wheee.