This is getting very close to spam...and you all have way too much time on your hands. Is there any situation where .99999999999999999 couldn't be called 1? I mean a real life situation, not something stupid like 2/(1-x) and x can't = 1 but it can = .99 repeating. Actually, it can't really equal .99 repeating, because then the answer would be infinite....my brain hurtz.
Just divide the left side by 8933490320 + 9040340348993488934983498 and the right side by 1 SEE HOW SIMPLE IT IS<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
He isn't using circular logic, you are. He first defines x = 0.9999..., this is not what he is trying to prove. You can allways multiply, divide, add or subtract a number from both sides if you wish, this changes nothing if they are equal, and per definition we know x = 0.999.... <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd--> I never said he was using circular logic, I implied that he wasn't using algebra. You cannot under any circumstances do different operations to different sides of the equation. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> In his situation x=.<u>99</u>. So basically he <i>was</i> doing the same thing to both sides of the equation. Just look at it again and you will see.
[WHO]ThemYou can call me DaveJoin Date: 2002-12-11Member: 10593Members, Constellation
<!--QuoteBegin-Mantrid+Jun 19 2004, 11:38 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (Mantrid @ Jun 19 2004, 11:38 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> I'm standing by my philosophy view. When you consider mathematics doesn't represent anything real, its all quite trivial.
For example, without using math (as it refers only to unreal things), prove to me that there is one of "something". <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> The memory of the first time you read this sentence. You cannot deny it's existance and by definition is singular.
I can deny the existance of that memory, specifically because I know not the exact conditions of that memory, thus the memory has been tainted, thus it is different than the actual memory. For all intents and purposes that memory is gone, and can't affect anything any longer. An object that can not compel change is logically unreal.
This memory of the sentence is present, but it is distinct from the original. I know of the previous existance of the memory, but not of the memory itself.
Now this may be because I'm tired, but I propose that the memory in question exists while at the same time it does not.
[WHO]ThemYou can call me DaveJoin Date: 2002-12-11Member: 10593Members, Constellation
<!--QuoteBegin-Mantrid+Jun 19 2004, 11:56 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (Mantrid @ Jun 19 2004, 11:56 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> For all intents and purposes that memory is gone, and can't affect anything any longer. An object that can not compel change is logically unreal. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> Talking about it is proof of it still affecting change. Were it not to exist you would not speak of it.
Actually, that was written in reference to the more recent second memory.
And, to prove I have that memory, you first have to prove I exist. <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html//emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo-->
[WHO]ThemYou can call me DaveJoin Date: 2002-12-11Member: 10593Members, Constellation
<!--QuoteBegin-Mantrid+Jun 20 2004, 12:05 AM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (Mantrid @ Jun 20 2004, 12:05 AM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> Actually, that was written in reference to the more recent second memory.
And, to prove I have that memory, you first have to prove I exist. <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html//emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo--> <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> * [WHO]Them walks into a secret room behind the clothes in his closet.
* [WHO]Them walks up to a spooky computer
* [WHO]Them types for a while
* [WHO]Them smacks the enter key and gets up
* [WHO]Them walks out of the secret room and back to his PC
<!--QuoteBegin-[WHO]Them+Jun 19 2004, 10:09 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> ([WHO]Them @ Jun 19 2004, 10:09 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> Here's another reason why it's broken logic to think of 0.<u>9999</u> as a number that you can perform arithmetic on.
Multiplication by X, by definition, is a number added to itself X many times.
Consider the case of 0.<u>9999</u> multiplied by 2....
You get a number that is just slightly less than 2, everyone conceptually knows this to be true, but here's where your problem comes up.....
0.999 * 2 = 1.998 0.9999 * 2 = 1.9998
In the case of 0.<u>9999</u> * 2, WHERE IN THE HELL DID YOU JUST PUT THAT 8??!??!??!?!??!?!?!?
IN THE BURNING DEPTHS OF HELL, WHERE BAD MATHEMATICIANS GO, THAT'S WHERE! <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> Oh man... if only I could fit that into a resonably sized sig quote...
<!--QuoteBegin-Mantrid+Jun 19 2004, 08:53 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (Mantrid @ Jun 19 2004, 08:53 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> The whole .99... = 1 phenomenon is more of a philosophical matter rather than an algebraic, mainly because it forces you to try and accept two things that are mutually exclusive and yet both true at the same time. It also deals with a metaphysical aspect in that something incomplete is the same as a whole. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> ... or that something infinite (like a series, .99...) can "turn into" something finite(1).
I think this bothers people for the same reason infinity itself bothers people. It's a concept that cannot be seen in our daily lives. There are not infinity atoms in your room, seconds in your life, or bums on a bench. So it will continue to only exist as a concept that everyone is wary about, except those who have done way too many integrations as can be healthy. And then I would argue they are only comfortable with it because they have become complacent in their thoughts of what it is they're actually representing with that little sideways eight and little d before the x. Infinitely small steps are just as conceptually disorienting as infinity itself.
What if space and time turn out to be discrete? Calculus-etc will be purely imaginary. (no pun intended)
god come on this has been going on for 5 pages. <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html//emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo--> The best way to settle this is to ask any trustable source (math teacher, etc) and we'll have a vote.
The main problem here is that people have a problem with "infinity"
The thing with an infinite number of 9's is that there is no "last 9" to turn into an 8 when you multiply it by 2. That's because there would always be a 9 after any other 9, forever and forever and forever.
That is why when you multiply it by 10 you still get an infinite number of decimals, and not "infinite minus 1"
FamDiaper-Wearing Dog On A BallJoin Date: 2002-02-17Member: 222Members, NS1 Playtester, Contributor
<!--QuoteBegin-MedHead+Jun 20 2004, 05:59 AM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (MedHead @ Jun 20 2004, 05:59 AM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> There is a similar problem to this. Imagine the distance between point A and B is say, two feet. Now, pretend an object is resting at point A, and point B is the destination. The distance the object can travel is half the total remaining distance between point A and point B. The fact is, because numbers are infinite, they can be infinitely halved: the object will never reach point B. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> I believe you are referring to Zeno's Paradox. Or an easing function, because I am a filthy Flasher!
algebric: you cannot reach infinity, infinity is a concept. your argument is invalid.
round at ten billion digits: round 2/3 at ten billion digits and you end on a 7. add 0.333~333 to 0.666~667 and you get 1, not 0.999~999
c++: when you add two concepts, infinites or symbols and expect an integer result: compile error: possible loss of precision (line 14) if you try to use long/double/int/whatever or you try to cast, you're rounding. see above
check out gorged's new group:
I Gorged Your Mom [avatar] Beast Group: Temporarily Suspended Posts: 61 Member No.: 21361 Joined: 1-October 03
<!--QuoteBegin-juice+Jun 20 2004, 03:30 AM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (juice @ Jun 20 2004, 03:30 AM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> I think this bothers people for the same reason infinity itself bothers people. It's a concept that cannot be seen in our daily lives. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> It's easier to experience infinity at the small end, rather than the large.
For example: Time is continuous. Time can be into infinately small moments. Imagine seeing everything is slow motion. Every time you pick a slower speed for the passing of time you can always make a slower speed without reaching a stop.
ThansalThe New ScumJoin Date: 2002-08-22Member: 1215Members, Constellation
note the fact that my post was edited <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html//emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo-->
I am playing with you BM <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html//emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo-->
.9999_ is an approximation for 1. .99999_ does not really exist, its not a number. Just like .3333_ is an approximation for 1/3, .6666_ is an approximation for 2/3, etc, .9999_ is an approximation for 1.
Thus x = 0.9999... 10x = 9.9999... 10x - x = 9.9999... - 0.9999... 9x = 9 x = 1.
you CAN subtract x from one side and .9999_ from the other, this is merely substituting equals for equals (x = .9999_ remember?), which is fine and dandy. Notice how if you were to replace .3333_ repeating in place of .9999_ repeating you would end up with 1/3, which I'm sure many of you will agree is correctimundo.
x = .3333_ 10x = 3.3333_ 10x - x = 3.3333_ - .3333 9x = 3 x = 1/3
tada! .9999_ is an approximation to 1, which could bve considered the same thing as the number one. You can do this with any repeating decimal (even though they don't really exist, they are just approximations).
<!--QuoteBegin-6john6doe6+Jun 20 2004, 08:21 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (6john6doe6 @ Jun 20 2004, 08:21 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> wrongo, an approximation is not the same as.
.99_ might be approximately 1, but it is still .99_ and not 1. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> exactly
Comments
Yes you can.
Just divide the left side by 8933490320 + 9040340348993488934983498 and the right side by 1 SEE HOW SIMPLE IT IS<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
He isn't using circular logic, you are. He first defines x = 0.9999..., this is not what he is trying to prove. You can allways multiply, divide, add or subtract a number from both sides if you wish, this changes nothing if they are equal, and per definition we know x = 0.999.... <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
I never said he was using circular logic, I implied that he wasn't using algebra. You cannot under any circumstances do different operations to different sides of the equation. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
In his situation x=.<u>99</u>. So basically he <i>was</i> doing the same thing to both sides of the equation. Just look at it again and you will see.
For example, without using math (as it refers only to unreal things), prove to me that there is one of "something".
For example, without using math (as it refers only to unreal things), prove to me that there is one of "something". <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
The memory of the first time you read this sentence. You cannot deny it's existance and by definition is singular.
This memory of the sentence is present, but it is distinct from the original. I know of the previous existance of the memory, but not of the memory itself.
Now this may be because I'm tired, but I propose that the memory in question exists while at the same time it does not.
Talking about it is proof of it still affecting change. Were it not to exist you would not speak of it.
And, to prove I have that memory, you first have to prove I exist. <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html//emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo-->
And, to prove I have that memory, you first have to prove I exist. <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html//emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo--> <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
* [WHO]Them walks into a secret room behind the clothes in his closet.
* [WHO]Them walks up to a spooky computer
* [WHO]Them types for a while
* [WHO]Them smacks the enter key and gets up
* [WHO]Them walks out of the secret room and back to his PC
....no I don't.
Multiplication by X, by definition, is a number added to itself X many times.
Consider the case of 0.<u>9999</u> multiplied by 2....
You get a number that is just slightly less than 2, everyone conceptually knows this to be true, but here's where your problem comes up.....
0.999 * 2 = 1.998
0.9999 * 2 = 1.9998
In the case of 0.<u>9999</u> * 2, WHERE IN THE HELL DID YOU JUST PUT THAT 8??!??!??!?!??!?!?!?
IN THE BURNING DEPTHS OF HELL, WHERE BAD MATHEMATICIANS GO, THAT'S WHERE! <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
Oh man... if only I could fit that into a resonably sized sig quote...
... or that something infinite (like a series, .99...) can "turn into" something finite(1).
I think this bothers people for the same reason infinity itself bothers people. It's a concept that cannot be seen in our daily lives. There are not infinity atoms in your room, seconds in your life, or bums on a bench. So it will continue to only exist as a concept that everyone is wary about, except those who have done way too many integrations as can be healthy. And then I would argue they are only comfortable with it because they have become complacent in their thoughts of what it is they're actually representing with that little sideways eight and little d before the x. Infinitely small steps are just as conceptually disorienting as infinity itself.
What if space and time turn out to be discrete? Calculus-etc will be purely imaginary. (no pun intended)
The best way to settle this is to ask any trustable source (math teacher, etc) and we'll have a vote.
The main problem here is that people have a problem with "infinity"
The thing with an infinite number of 9's is that there is no "last 9" to turn into an 8 when you multiply it by 2. That's because there would always be a 9 after any other 9, forever and forever and forever.
That is why when you multiply it by 10 you still get an infinite number of decimals, and not "infinite minus 1"
I believe you are referring to Zeno's Paradox. Or an easing function, because I am a filthy Flasher!
algebric:
you cannot reach infinity, infinity is a concept. your argument is invalid.
round at ten billion digits:
round 2/3 at ten billion digits and you end on a 7.
add 0.333~333 to 0.666~667 and you get 1, not 0.999~999
c++:
when you add two concepts, infinites or symbols and expect an integer result:
compile error: possible loss of precision (line 14)
if you try to use long/double/int/whatever or you try to cast, you're rounding. see above
check out gorged's new group:
I Gorged Your Mom
[avatar]
Beast
Group: Temporarily Suspended
Posts: 61
Member No.: 21361
Joined: 1-October 03
It's easier to experience infinity at the small end, rather than the large.
For example: Time is continuous. Time can be into infinately small moments. Imagine seeing everything is slow motion. Every time you pick a slower speed for the passing of time you can always make a slower speed without reaching a stop.
Also: [WHO]Them is right.
not 1
not 0.9
not 0.8
not 7642
0.9999 recurring
not 1
not 0.9
not 0.8
not 7642
0.9999 recurring <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
exactly.
for all instents and purposes, .9 recuring = 1
simple, aint it?
<!--emo&:p--><img src='http://www.unknownworlds.com/forums/html//emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo-->
for intensive purposes 0.999~999 == 0.999~999
and if you replace "infinity" with "ten billion" then 0.999~999 is 1 because 0.333~333 + 0.666~667 = 1
<!--emo&:p--><img src='http://www.unknownworlds.com/forums/html//emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo-->
i have to deal with a hellalotta typos, so i read words as what the guy may have meant instead of what's actually there
I am playing with you BM <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html//emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo-->
not 1
not 0.9
not 0.8
not 7642
0.9999 recurring <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
/me slaps the number system
lim(m --> ∞) sum(n = 1)^m (9)/(10^n) = 1
0.9999... = 1
Thus x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.
you CAN subtract x from one side and .9999_ from the other, this is merely substituting equals for equals (x = .9999_ remember?), which is fine and dandy. Notice how if you were to replace .3333_ repeating in place of .9999_ repeating you would end up with 1/3, which I'm sure many of you will agree is correctimundo.
x = .3333_
10x = 3.3333_
10x - x = 3.3333_ - .3333
9x = 3
x = 1/3
tada! .9999_ is an approximation to 1, which could bve considered the same thing as the number one. You can do this with any repeating decimal (even though they don't really exist, they are just approximations).
.99_ might be approximately 1, but it is still .99_ and not 1.
.99_ might be approximately 1, but it is still .99_ and not 1. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
exactly
Can't juggle with infinite numbers unless you're dealing with limit values (at least I think that's what it's called, not sure of the english term)
0,<u>9999</u> != 1
What you're basically proving is that
lim(x) = 1
x-->1-
And well, that's pretty obvious.
Unless you want me to prove that the hyperbola f(x)=1/x collides with the x-axis in infinity? Which pretty much defies definitions.