Motion is impossible. - Page 3
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HnR)hT
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United States3468 Posts
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Chaso
Sweden143 Posts
On July 25 2005 05:55 Xeofreestyler wrote: Achilles and the turtle. It wasn't a rabit. My bad. | ||
ULIKEIT
United States44 Posts
On July 25 2005 05:55 Xeofreestyler wrote: Achilles and the turtle. It wasn't a rabit. Your right but for all the other kids out there it was warners brothers early version of bugs bunny and the turtle. | ||
Hippopotamus
1914 Posts
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BigBalls
United States5354 Posts
sum(n=1 to infinity) (1/2^n) = 1. There are a number of proofs of this. If you want one, Ill post one later. | ||
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Bill307
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Canada9103 Posts
On July 25 2005 04:38 jtan wrote: An infinite amount of intervals that are getting infinitly small equals a finite lenght ![]() Wrong. 1 + 1/2 + 1/3 + 1/4 + 1/5 + ... diverges to infinity, evening though the intervals are getting infinitely small. There are a number of ways to determine whether a series converges to a finite number or diverges to infinity. That's calculus 2 ![]() Btw BigBalls is right. And probably some other people as well, but his answer was particularly terse ![]() | ||
Sorrow_eyes
United States1007 Posts
There are infinite amounts of half points, but the total time it takes to run is finite. The time it takes to reach the next half point will be shorter and shorter. Therefore the runner finish the run. | ||
NewbSaibot
3849 Posts
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IntoTheWow
is awesome32277 Posts
On July 25 2005 19:18 NewbSaibot wrote: There is no such thing as infinity, it is something man made up. Everything is finite, time, the universe, this senten..... prove? | ||
Hippopotamus
1914 Posts
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LetMeBeWithYou
Canada4254 Posts
On July 25 2005 19:18 NewbSaibot wrote: There is no such thing as infinity, it is something man made up. Everything is finite, time, the universe, this senten..... Human stupidity =] On July 25 2005 19:24 Hippopotamus wrote: What about your ego? that's close to infinite since he will die | ||
teh leet newb
United States1999 Posts
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Tontow
United States73 Posts
-500 meters is still equal to 500 meters no matter how you split it up. Kochen said it first and its basic math: What you do to one side or part of the equation you must do to the other side or part of the equation. If you divide distance an infinite amount of times, then you must divide time an infinite amount of times. 500M / infinitely = time to run 500M / infinitely -However, It is also mathematically feasible to prove Zeno correct. Assuming that we are dividing “time” an infinite amount of times, then somewhere along the line there is bound to be a repeating decimal. 3. Zeno points out, given that we are assuming that space is continuous, Now, here is where it gets tricky. The following formula stats that any that any decimal that repeats -- (and ,thus, is infinite) – will infinitely approach and equal the next highest whole number, thus rounding it up. (Note: the proof was confirmed by my college math teacher.) http://www.blizzard.com/press/040401.shtml 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 must also look at the perception point of view. You perceive a single grain of rice falling; if you use an amplifier you can perceive the sound that that grain makes. The same goes for a bag of rice. In this case the question is, “Are we perceiving that the runner is going from point A to point B? Or is he actually moving from point A to point B? Is it possible that both could be true?” I hope this helps with your essay. | ||
SweeTLemonS[TPR]
11739 Posts
On July 24 2005 23:19 baal wrote: wow i tought intelligent people would understand the concept of infinite IN infinites. Ill put it in a veeeery simle way to explain it. Imaginte an INFINITE row of 1 dollar bills, now: Imagine an INFINITE row of 100 dollar bills, just under the 1 dolar row, 1 : 1 ratio right? So in wich of those you have more money?, well you might think, in the $100 bill row right? but how? if you have INIFINITE money on the other one? errr... confusing? SIMPLE, there are infinites in infinites, i cant remember the whole formula to prove it, can someone post it? But the 100 is also infinite, meaning it will go on and on for as long as the $1 line does, right? So, let's just take a small portion of that and end at 1,000. You have either $1,000 or $100,000. I don't see how you could say that the $1 line has the same amount of money as the $100 line. | ||
WOstick
Norway433 Posts
[/QUOTE] But the 100 is also infinite, meaning it will go on and on for as long as the $1 line does, right? So, let's just take a small portion of that and end at 1,000. You have either $1,000 or $100,000. I don't see how you could say that the $1 line has the same amount of money as the $100 line.[/QUOTE] You foiled it all when you said a small portion of that line. What he was saying was that infinate is infinate. You cant multiply infinity in the same way. infinate times a million still equals infinate. When speak about a small portion of these lines, they are no longer infinate. | ||
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Rekrul
Korea (South)17174 Posts
On July 26 2005 08:54 SickofLife wrote: But the 100 is also infinite, meaning it will go on and on for as long as the $1 line does, right? So, let's just take a small portion of that and end at 1,000. You have either $1,000 or $100,000. I don't see how you could say that the $1 line has the same amount of money as the $100 line. PLEASE TELL ME YOUR JOKING LOLLLLLLLLLLLLL thats the whole idea behind the concept of infinity ITS NOT SOMETHING THE HUMAN BRAIN CAN COMPREHEND, IT DOESN'T MAKE SENSE | ||
BigBalls
United States5354 Posts
here is a bit of a trickier example. Define Z+ = the positive integers. So Z+ = {1,2,3,.....} 2*Z+ = {2,4,6,.....}, the even positive integers. Now, 2*Z+ is a SUBSET of Z+. This means that every element in 2Z+ is an element of Z+. It is a proper subset, meaning there are elements in Z+ that are not in 2Z+. Both of these sets are the same size. Thus, there exists a 1 to 1 and onto map between these two sets, which is known as a bijection. Thus, there is an infinite set which is a subset of another infinite set, and can be mapped 1-1 AND onto it. To move into analysis, take the interval (0,1). (0,1) is NOT countable, there are an infinite number of elements in there. furthermore, any interval is not countable, as long as it has positive measure then it is infinite. However, the example before, 2Z+ IS countable. Although it has an infinite number of elements, it has measure 0. Infinity is kind of weird, but to me these concepts are intuitive. But yeah, being on topic, Zeno's proof falls apart when he makes a false assumption. This was often referred to as Zeno's paradox, because SUM_(n=1 to infinity) (.5^n) = 1. | ||
Tontow
United States73 Posts
On July 26 2005 10:21 BigBalls wrote: But yeah, being on topic, Zeno's proof falls apart when he makes a false assumption. This was often referred to as Zeno's paradox, because SUM_(n=1 to infinity) (.5^n) = 1. Its lim(m --> ∞) sum(n = 1)^m (9)/(10^n) = 1 ...... Infinite 1 dollar is equal to infinite 100 dollars. And, Zeno is talking about an infinitely small portion of infinity, but -However, It is also mathematically feasible to prove Zeno correct. Assuming that we are dividing “time” an infinite amount of times, then somewhere along the line there is bound to be a repeating decimal. -------------------------------------------------------------------------------- 3. Zeno points out, given that we are assuming that space is continuous, -------------------------------------------------------------------------------- Now, here is where it gets tricky. The following formula stats that any that any decimal that repeats -- (and, thus, is infinite) – will infinitely approach and equal the next highest whole number, thus rounding it up. (Note: the proof was confirmed by my college math teacher.) http://www.blizzard.com/press/040401.shtml 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. I think the answer is to be shown as: -2 -1 0 1 2 <---------------------------------------------------------------------------> (0 < (X / infinity) <_ 1) / infinity (0 is smaller than (X divided by infinity), (X divided by infinity) is smaller than or equal to 1) divided by infinity. | ||
BigBalls
United States5354 Posts
http://mathworld.wolfram.com/ZenosParadoxes.html | ||
Krzych
Poland693 Posts
On July 26 2005 10:13 Rekrul wrote: PLEASE TELL ME YOUR JOKING LOLLLLLLLLLLLLL thats the whole idea behind the concept of infinity ITS NOT SOMETHING THE HUMAN BRAIN CAN COMPREHEND, IT DOESN'T MAKE SENSE It does make sense! take this for example: lim [n->oo] (100n)/n = ? do you think it equals 1 because you have infinity in numerator and denominator? | ||
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