Report, edit, etc...Posted by ZPD on 2006-02-25 at 13:15:20
But the logic for the second velocity must be flawed because the rabbit is capable of moving past the turtle, it shows that the idea is false. Time doesn't pass in snapshots either, if that was true with this idea of breaking things in half infinitely, then all motion would follow a curve where times seems to mvoe slower and aloswer but never completely stop. The rabbit isn't going to be restricted by the movements of the turtle unless the amount of allocated time is too little for the rabbit to do so.
It would also depend on the kind of paper though, I bet you could fold a tissue more than 8 times, and you could fold it even more times if you cut it up and folded each of the pieces,
.
QUOTE
It's impossible to fold a piece of paper in half more than eight times.
That just shows you can't impose the idea of breaking things down forever in a world governed by the physics we have on Earth.It would also depend on the kind of paper though, I bet you could fold a tissue more than 8 times, and you could fold it even more times if you cut it up and folded each of the pieces,
.Report, edit, etc...Posted by justin_grant on 2006-02-27 at 02:27:46
Ok I know I quit this site, but google showed me this page.
No it wont, as it will go
1/2,
1/4
1/8
1/16
1/36
And so on, thus it will never be able to make it.
No it wont, as it will go
1/2,
1/4
1/8
1/16
1/36
And so on, thus it will never be able to make it.
Report, edit, etc...Posted by EzDay281 on 2006-02-27 at 19:36:22
Too lazy to read the second page, but the answer is as variable as the 'Does 0.999...=1?' question.
The difference between 0.999... and 1 is infinitely small.
So, you could say that 0.999...=1, because 1-(0.0...1•999...[infinity])=1.
Or, you could say that, because that 0.0...1 difference is still there, it's not equal to one.
Both questions are the same, since they're both effectively 'is an infinitely small difference equal to no difference and thus congruency?'.
The difference between 0.999... and 1 is infinitely small.
So, you could say that 0.999...=1, because 1-(0.0...1•999...[infinity])=1.
Or, you could say that, because that 0.0...1 difference is still there, it's not equal to one.
Both questions are the same, since they're both effectively 'is an infinitely small difference equal to no difference and thus congruency?'.
Report, edit, etc...Posted by A_of_s_t on 2006-03-03 at 20:19:03
DAMN, LOOK AT ALL THE POSTS.
I forget about this forum for a week and there are tens of people argueing about a simple paradox. It is hard fot the human brain to grasp this concept, I know:
An infinite series of numbers equals 1.
It is very hard to try this and even harder to do.
I forget about this forum for a week and there are tens of people argueing about a simple paradox. It is hard fot the human brain to grasp this concept, I know:
An infinite series of numbers equals 1.
It is very hard to try this and even harder to do.
Report, edit, etc...Posted by BeeR_KeG on 2006-03-03 at 20:26:12
The answer is:
lim[sub](x-->0)[/sub] f(x)+C/x , C does not equal 0, lim[sub](x-->0)[/sub] f(x) = 0
lim[sub](x-->0)[/sub] f(x)+C/x , C does not equal 0, lim[sub](x-->0)[/sub] f(x) = 0
Report, edit, etc...Posted by A_of_s_t on 2006-03-03 at 20:28:33
What? Ok, let's see, limit (?) is x going to 0... what is the
QUOTE
f(x)+C/x
Report, edit, etc...Posted by pekkel_the_duck on 2006-03-03 at 20:29:39
Just aim at something very far but directly behind the target. O.o
Report, edit, etc...Posted by A_of_s_t on 2006-03-03 at 20:31:01
Ok, I found the origanal website:
Puzzle 3
You can imagine an arrow in flight, toward a target. For the arrow to reach the target, the arrow must first travel half of the overall distance from the starting point to the target. Next, the arrow must travel half of the remaining distance.
For example, if the starting distance was 10m, the arrow first travels 5m, then 2.5m.
If you extend this concept further, you can imagine the resulting distances getting smaller and smaller. Will the arrow ever reach the target?
Answer:Yes. This is because the sum of an infinite series can be a finite number. Thus, 1/2 + 1/4 + 1/8 + ... = 1 and the arrow hits the target.
Puzzle 3
You can imagine an arrow in flight, toward a target. For the arrow to reach the target, the arrow must first travel half of the overall distance from the starting point to the target. Next, the arrow must travel half of the remaining distance.
For example, if the starting distance was 10m, the arrow first travels 5m, then 2.5m.
If you extend this concept further, you can imagine the resulting distances getting smaller and smaller. Will the arrow ever reach the target?
Answer:Yes. This is because the sum of an infinite series can be a finite number. Thus, 1/2 + 1/4 + 1/8 + ... = 1 and the arrow hits the target.
Report, edit, etc...Posted by olaboy- on 2006-03-03 at 20:37:12
This kind of sounds like absolute time and half-lifes...
Report, edit, etc...Posted by A_of_s_t on 2006-03-03 at 20:42:20
Yo, I just gave u the Ultimate answer, I guess I should close this shouldn't I...?
Report, edit, etc...Posted by Raindodger on 2006-03-03 at 23:40:04
QUOTE
Answer:Yes. This is because the sum of an infinite series can be a finite number. Thus, 1/2 + 1/4 + 1/8 + ... = 1 and the arrow hits the target.
Isn't that like the same debate going on that .999~ = 1. So couldnt that be arguable?
Report, edit, etc...Posted by Shadow-Killa_04 on 2006-03-04 at 01:50:08
No it will technicaly never reach obviously. Yes, it will get .0000000000001 nanometers away but it will never touch. And yes, you could assume that it touches at that point. I don't see to much of a discussion here.
Report, edit, etc...Posted by A_of_s_t on 2006-03-04 at 19:10:25
My thread was made before that one Shady.
Report, edit, etc...Posted by Wilhelm on 2006-03-05 at 04:05:09
Measurements are arbitrary and relative.
Report, edit, etc...Posted by DT_Battlekruser on 2006-03-05 at 13:21:54
QUOTE(Demaris @ Feb 19 2006, 09:56 PM)
Actually, when it hits an angstrom away, the next step it will touch it.
An angstrom is the smallest piece that the universe can be divided into
Its 10[sup]-42[/sup] meters I think.
[right][snapback]431135[/snapback][/right]
An angstrom is 10[sup]-10[/sup] meters.
The answer is yes, the arrow will hit the target. If you take "the whole distance" that you're having to be th distance from the nucleus of the atom of the tip of the arrow to the nucleus of the atom on the target, when they are a very small distance apart (which will happen), the electromagnetic fields will repulse eachother and the arrow will "hit" the target.
QUOTE
So, you could say that 0.999...=1, because 1-(0.0...1•999...[infinity])=1.
(0.000.......1 = 0.) (999...... = ∞). 0•∞ is indeterminate. 1-(0•∞) is not 1.
Report, edit, etc...Posted by BeeR_KeG on 2006-03-05 at 14:25:25
From a Physics point of view, as DTBK stated, yes, it will hit the target. But from plain logical and mathematical contact, no.
Report, edit, etc...Posted by A_of_s_t on 2006-03-05 at 22:38:35
I made a program to show it works out of a game programming kit.
I made it say...
What came up was and error, saying that overtime flow had happened, I debugged it and it said that too many calculations were being made...
I made it say...
CODE
x = ()
.This lets a person type a number
.The number I typed was 1
Display = ( 1/2 x )
x = ( 1/2 x )
t = ( t +x )
Return
.The next couple of 'actions' are confusing, I'll leave them out, what those did was make the program stop at anytime that I type 's' and display 't'
.This lets a person type a number
.The number I typed was 1
Display = ( 1/2 x )
x = ( 1/2 x )
t = ( t +x )
Return
.The next couple of 'actions' are confusing, I'll leave them out, what those did was make the program stop at anytime that I type 's' and display 't'
What came up was and error, saying that overtime flow had happened, I debugged it and it said that too many calculations were being made...
Report, edit, etc...Posted by chrono_seifer on 2006-03-06 at 00:04:00
QUOTE(Falcon_A @ Feb 19 2006, 09:43 PM)
Obviously not.
It will eventually become incredibly close to the target but be moving so slowly, it might look as if it has hit it when it is indeed just floating in hte air next to it.
But it will never hit. =/
ADDITION:
you may be more like.... x to the 1/2 power of the distance or something if you want an actual formula...
but it eventually goes to like 1/1000000000000000000000000th of a millimeter away, as you could imagine.
[right][snapback]431014[/snapback][/right]
It will eventually become incredibly close to the target but be moving so slowly, it might look as if it has hit it when it is indeed just floating in hte air next to it.
But it will never hit. =/
ADDITION:
you may be more like.... x to the 1/2 power of the distance or something if you want an actual formula...
but it eventually goes to like 1/1000000000000000000000000th of a millimeter away, as you could imagine.
[right][snapback]431014[/snapback][/right]
ummm no it wont?
ADDITION:
QUOTE(BeeR_KeG @ Mar 5 2006, 01:25 PM)
From a Physics point of view, as DTBK stated, yes, it will hit the target. But from plain logical and mathematical contact, no.
[right][snapback]439838[/snapback][/right]
[right][snapback]439838[/snapback][/right]
u see?
Report, edit, etc...Posted by A_of_s_t on 2006-03-06 at 19:03:39
Mmmm... why does a leginimate website say that it will hit, if you say it doesn't?
Report, edit, etc...Posted by BeeR_KeG on 2006-03-06 at 19:33:31
Physcs point of view:
You have object A traveling at V velocity going towards object B. The distance per time unit will always be traveling at half the distance necesary to reach object B. Object A and B both have a gravitational and magnetic field. Once object A reaches a critical point, they will both be attracted to each other. There will also be a point when the tip of the arrow gets inside the electron's field of the atoms, which is also considered coliision.
Mathematical point of view:
Discrading all the gravity, magnetism, electrons and such, we would have this: Object A travels toward coordinates (x,y,z) and per time unit, will always travel half of what is needed to reach (x,y,z). Since I can divide a number by half as many times as I want, I have infinite possibilities to divide the distance, but never reaching there.
You have object A traveling at V velocity going towards object B. The distance per time unit will always be traveling at half the distance necesary to reach object B. Object A and B both have a gravitational and magnetic field. Once object A reaches a critical point, they will both be attracted to each other. There will also be a point when the tip of the arrow gets inside the electron's field of the atoms, which is also considered coliision.
Mathematical point of view:
Discrading all the gravity, magnetism, electrons and such, we would have this: Object A travels toward coordinates (x,y,z) and per time unit, will always travel half of what is needed to reach (x,y,z). Since I can divide a number by half as many times as I want, I have infinite possibilities to divide the distance, but never reaching there.
Report, edit, etc...Posted by Killer_Kow(MM) on 2006-03-15 at 19:48:38
Of coure it would hit the target, I'd get mad for it going so slow, grab the arrow and shove it into the target.
Also, for the angstrom thing. In my opinion, you can always get smaller. For example: think of the smallest dot you can think of in your head. Now magnify that dot, move it aside and create another small dot. You can do this forever, so whos to say it can't be done in reality?
^Just my opinion...
Also, for the angstrom thing. In my opinion, you can always get smaller. For example: think of the smallest dot you can think of in your head. Now magnify that dot, move it aside and create another small dot. You can do this forever, so whos to say it can't be done in reality?
^Just my opinion...