how can our hands clap together if they have to cover an infinite amount of steps? i get that each step is halved, but doesn't each step still take a finite amount of time?
basically you have this 1 meter approach, where each interval is 1, 1/2,1/4/,1/8, and so on.
you sum up the terms to get 1+1/2+1/4+1/8+... and so on, you get a sum S.
with 1/2S you get 1/2+1/4+1/8+...
S-1/2S=1 since all the other terms cancel, i get that too; you get S(1-1/2)=1 =>1/2S=1=>S=2
this means your hands cover 2 meters. ok great.
but this means that you covered an infinite amount of steps.
how the FUCK is that done in a finite amount of time? at some point those steps would have to be instant or violate the speed of light and other shit. how is this hand-waived as just being a simple paradox that calculus (((((((solved)))))))???
Matthew Robinson
the sum of infinitely many finite numbers is not necessarily infinite. So infinitely many steps doesn't have to mean infinite time. If you're too dumb to understand it then instead just get used to it
this stupid idea should never be taught without first prefacing it with limits of precision.
Tell me anons, how do you halve a plank length.
David Cruz
This problem is called a p series and is convergent which is the reason why it doesn't take an infinite amount of time. This is calc 2, you'll get to it in high school
Jacob Walker
(plank lenght)/2
brainlet
James Smith
If you are truly considering every one of these infinite steps as a step made by the motion of a hand, then consider this. The distance of step n = 1/(2^n) so as n approaches infinity the distance approaches 1/(2^infinity) which approaches 0. This means not all of the infinite steps take more than 0 distance so there are a finite amount of steps of greater than 0 distance.
Joshua Baker
because math only conceptually models reality
there is no "half" distance crossed, there is only one length crossed, the planck length
Logan Kelly
None of the terms in the sequence, by definition, are equal to zero. This is either shit tier bait, or you need to reconcile your understanding of infinity and convergence.
Bentley Bell
>can't spell "length" brainlet
Landon Wright
>can't spell "Planck" brainlet
Tyler Morales
1 =1/2+1/2 =1/2+1/4+1/4 =1/2+1/4+1/8+1/8 =1/2+1/4+1/8+1/16+1/16 =1/2+1/4+1/8+1/16+1/32+1/32 etc.
Cameron Sanchez
they approach zero see in my post >which approaches 0
But anyway, limits of precision make this irrelevant. There's physically a point where division is impossible and the problem breaks down.
Connor Russell
Utter gibberish. Half a planck is half a planck. Whats stops its existence? Name one contradiction.
Carter Rivera
Even if you were to somehow re-frame this "problem" into a situation where there could possibly be infinite division, it's still not a problem. By pointing out that there's a physical limitation that prevents infinite division, you're avoiding the real core of the misunderstanding. There is an underlying conceptual mistake that's more much important to correct than just pointing out some pedantic detail about planck lengths. If somebody can't overcome Zeno's Paradox without resorting to planck length then they are showing a failure of understanding the summing of infinite sets.
Noah Long
This is called Zeno's paradox. There's been a lot written about it and a lot of possible solutions.
Bottom line is if you believe in general relativity there is no reason to consider time and space as separate entities anyway. This problem is a non-starter
Austin Murphy
Dumbest post in this thread. How does relativity work here were talking about distance not motion.
Cooper Ortiz
>not all of the steps have distance greater than 0
This literally means that you think there are some steps which have 0 or less than 0, which is wrong.
All of the terms are greater than 0. But it doesn't take infinite time to approach 0, as has already been stated.
Wyatt Jackson
This. There is a minimum size limit to the universe, 'pixels' if you will, therefore nothing can move at distances smaller.
Nathaniel Lewis
if you literally think there are no steps of 0 distance then you literally think there are infinity steps
>infinity steps >all nonzero distance choose only one
Alexander Clark
Really, it's trivial. Suppose your hands are moving at one meter per second. Ignoring the paradox for now, we can see that we would complete the clap after 2 seconds. If we look at it in the lens of the paradox now, the first step is completed in 1 second, the second in half a second, the third in a quarter, and so on. Clearly this sums to a finite number, 2, while the speed never exceeded one meter per second.
Connor Myers
But george canteen said in his diagonalization augment that the set of all natural numbers cant form an erection with the set of all second numbers.
Isaiah Ross
Brainlet, your hands never actually touch but it squeezes the air to a point that it compresses and rushes out of the gaps. Hence the pop or clap that you hear.
Zachary Phillips
time is infinitely divisible, so we can perform an infinite number of steps in some span of time because there are an infinite number of time steps for us to do it in.
Evan Scott
So then no time passes???
Oliver Baker
division doesn't really exist
nothing can actually be divided as nothing actually exists besides tiny indivisible dots. splitting something is nothing more than to simply separate the constituents of that something away from one another. you can't split something that is not made up of smaller parts.
Parker Martinez
>this is what brainlets actually believe An infinite amount of time passes because it is infinitely divisible.
Leo Allen
You need to learn about convergence theorem. Stop trying to explain something is taught in high school and you clearly have no understanding of.
Samuel Foster
What the fuck. If i have a piece of bread and divide it infinite times then i have infinite bread. But i started off with finite bread....
Elijah Bell
Something that is infinitely divisible does not need to be infinite in size. There are an infinite number of points between 0 and 1, but we know that the magnitude of the difference between these two points is sill only 1.
Christopher Jackson
...
Nicholas Carter
if you aren't going to try to explain yourself i'll just assume you have nothing else to support your point
Jayden Davis
But then every piece is zero. So you have a sum of zero. Which zero. How can this be?
Charles Rivera
If your unit precision is only .01, there are only 100 points between 0 and 1.
Alexander Phillips
please show me as to where i can find said infinite points in reality. where is it located?
Jacob Cruz
>Requiring a real-life analog to understand a mathematical axiom Get out of here brainlet
Parker Scott
...
Bentley Barnes
hmm i thought mathematics was the language of the universe? that it described reality? surely you should be able to find an example somewhere in the realm of reality?
Camden Perry
It's simple: the axiom of infinity is pure buffoonery.
Brody Gonzalez
I do not believe that mathematics is the language of the universe. It is a system that is very useful for describing the universe. The presence of characteristics that don't translate to reality does not change its usefulness or ability to describe reality.
Jayden Richardson
Your statements only work if you don't have an actual amount if tine it takes for you to clap. If it takes 1 second, then every step takes x per second.