Anonymous at Mon, 8 Jul 2024 17:39:30 UTC No. 16273020

>>16272987
infinite series finite sum

Anonymous at Mon, 8 Jul 2024 18:30:31 UTC No. 16273058

>Zeno devised these paradoxes to support his teacher Parmenides's philosophy of monism, which posits that despite our sensory experiences, reality is singular and unchanging. The paradoxes famously challenge the notions of plurality (the existence of many things), motion, space, and time by suggesting they lead to logical contradictions.
Very based.

Anonymous at Mon, 8 Jul 2024 18:54:55 UTC No. 16273076

>>16272987
There's no paradox though.

Anonymous at Mon, 8 Jul 2024 19:31:21 UTC No. 16273127

>>16272987
Distance in real life is not infinitely divisible
Distance mathematically can use limits at infinity
There is no problem

Anonymous at Mon, 8 Jul 2024 20:46:02 UTC No. 16273212

>>16272987
mathematicians actually believe an infinite sum is actually possible LMAO

Anonymous at Mon, 8 Jul 2024 20:47:31 UTC No. 16273214

>>16272987
Like you, most people don’t understand the purpose of said paradox because it wasn’t meant to be taken alone, but along with the other 2. The Achilles/Tortoise says that space/time is discrete because IRL you can’t go half distances infinitely many times, and on the other hand the Arrow paradox says that if space/time is discrete, then motion shouldn’t be possible. The paradox wasn’t solved obviously. All these calculus books and instructors who claim that calculus solves the Achilles/tortoise problem are clueless as they didn’t understand Zeno’s point to begin with… the paradoxes are to be taken together and it’s very subtle

Anonymous at Mon, 8 Jul 2024 21:21:17 UTC No. 16273242

>>16273214
>Arrow paradox says that if space/time is discrete, then motion shouldn’t be possible.
Please study Newton's laws of motion.

Anonymous at Mon, 8 Jul 2024 21:26:58 UTC No. 16273251

>>16273127
>Distance in real life is not infinitely divisible
>implying

Anonymous at Mon, 8 Jul 2024 21:32:58 UTC No. 16273263

>>16272987
Not so clever in the age of quantum mechanics but 2000 years ago this had little greek fancyboys pissing themselves. Zeno was up to his neck in bussy.

Anonymous at Mon, 8 Jul 2024 21:36:18 UTC No. 16273271

>>16273214
e pur si muove

Anonymous at Mon, 8 Jul 2024 21:36:25 UTC No. 16273272

>>16273242
>Newton’s laws
lol, it’s not a law darling, it’s an inaccurate model, it’s a gross approximation of how some of the world works. you can’t explain the atom with muh Newton’s “laws” kek. please go study QM

Anonymous at Mon, 8 Jul 2024 21:41:03 UTC No. 16273279

>>16273251
Go ahead, run half a Planck length. Let us know how that works out for you.

Anonymous at Mon, 8 Jul 2024 21:43:03 UTC No. 16273284

>>16273272
Cope more midwit. The existence of relativity does not negate the classical model in everyday uses. Telling a philosopher to study quantum mechanics is animal cruelty.

Anonymous at Mon, 8 Jul 2024 21:55:04 UTC No. 16273301

>>16272987
solution
>achilles IS the tortoise

Anonymous at Mon, 8 Jul 2024 23:03:54 UTC No. 16273368

>>16273284
>Telling a philosopher to study quantum mechanics is animal cruelty.
Then don’t philosophize about physics because QM *is* physics. Also Newton’s “law” is derived from QM as a series of approximations. If you want to understand what newton’s 2nd law implies you have to understand QM: https://www.eftaylor.com/pub/QMtoNewtonsLaws.pdf
>The existence of relativity does not negate the classical model in everyday uses.
What are you babbling about? The discussion revolves about what reality is at its smallest scales, that’s what Zeno’s paradoxes are about. It’s whether or not time and space are discrete or continuous. These are small scales where classical mechanics and relativity don’t operate or are INVALID. You’re confused bud.

Anonymous at Mon, 8 Jul 2024 23:24:25 UTC No. 16273400

>>16273127
>Distance in real life is not infinitely divisible
Angles are. You could duplicate the paradox with rotation.

Anonymous at Mon, 8 Jul 2024 23:31:45 UTC No. 16273409

>>16272987
In every stage achilles catches the point where the tortoise was and for the next stages it takes less and less time untill at some point the +time turns to -time and achilles passes the tortoise

Anonymous at Tue, 9 Jul 2024 00:03:41 UTC No. 16273437

>>16272987
Most are fucktarded enough to think .9... is 1

raspberry pie at Tue, 9 Jul 2024 00:08:47 UTC No. 16273445

>>16273214
>you can’t go half distances infinitely many times
*you can't go half distances infinity times
Fixed. Saying 'infinitely many' is a bloated and cluttered way of just saying what we already have a word for: Infinity. Anyone that ever uses the phrase 'infinitely many' is a turbo autist.

Anonymous at Tue, 9 Jul 2024 00:36:44 UTC No. 16273497

>>16273400
A rotating object is still bound to Planck’s constant. So, just as with linear distances you could theoretically divide it ad infinitum, in practice you’ll hit a limit eventually.

raspberry pie at Tue, 9 Jul 2024 00:50:25 UTC No. 16273512

>>16273272
>>16273284
Newtons laws are more accurate than QM and QM is more accurate than r*lativity

Anonymous at Tue, 9 Jul 2024 00:50:37 UTC No. 16273513

>>16273497
>>16273279
Planck lengths are just where measurement breaks down. There is no reason to believe it is the pixel size of the universe

Anonymous at Tue, 9 Jul 2024 01:03:51 UTC No. 16273526

>>16273127
You don't know that. What if they find shit smaller than quarks? What if it keeps going forever?

Anonymous at Tue, 9 Jul 2024 01:08:07 UTC No. 16273531

>>16273513
>where measurement breaks down
Cool it with the popsci, bro.
>There is no reason to believe it is the pixel size of the universe
Wrong. It is very reasonable to suspect that space is quantized and that a unit of space/length is Planck length. It would explain a lot (such as why light travels at c, if time is also quantized at the Planck scale, as that would then give light a velocity of 1 at the quantum level).

Anonymous at Tue, 9 Jul 2024 01:09:25 UTC No. 16273532

>>16273526
Quarks haven't even been 'found', only theorized. At such a small scale we can't actually prove it exists, we can only speculate.

Anonymous at Tue, 9 Jul 2024 01:24:33 UTC No. 16273544

>>16273531
>Cool it with the popsci, bro.
Current state of /sci/: the Heisenburg Uncertainty Principle is pop science
> It is very reasonable to suspect that space is quantized
No, because that would give rise to Lorentz violations and there have not been any found.
>It would explain a lot
Wishful thinking

Anonymous at Tue, 9 Jul 2024 01:43:08 UTC No. 16273569

>>16273544
>Heisenburg Uncertainty Principle is pop science
No, taking it out of context and misrepresenting it as measurement 'breaking down' is popsci. 95% of time physicists use the phrase 'break down', its popsci, and you know it.
>No, because that would give rise to Lorentz violations
Or our understanding is incomplete
>and there have not been any found.
Doesn't mean they don't exist
>Wishful thinking
It WOULD explain a lot. I am not definitively saying space and time are quantized, but you can't deny that if they are, it explains a lot.

Anonymous at Tue, 9 Jul 2024 01:48:44 UTC No. 16273577

>>16273497
>A rotating object is still bound to Planck’s constant
Which doesn't keep angles from being infinitely divisible. Which should really be obvious simply based on how angles of rotation are constructed in 3D space

Anonymous at Tue, 9 Jul 2024 01:59:51 UTC No. 16273590

>>16273531
>why light travels at c
For the same reason sound travels at mach 1

Anonymous at Tue, 9 Jul 2024 02:02:23 UTC No. 16273591

>what's the deal with this paradox involving an infinite sum of small values that was posited prior to the invention of integral calculus

Anonymous at Tue, 9 Jul 2024 02:14:05 UTC No. 16273602

>>16273591
>What's the deal with Achilles moving at a finite speed faster than the tortoise and then equal speed to the tortoise the moment he catches it at an exact calculable time?
Greek mathgeeks were as hated then as modern mathgeeks deserve abuse.

Anonymous at Tue, 9 Jul 2024 02:15:45 UTC No. 16273603

>>16273602
understanding that an infinite sum can converge hardly makes one a "mathgeek"

Anonymous at Tue, 9 Jul 2024 08:52:59 UTC No. 16273901

>>16272987
https://youtu.be/U0w0f0PDdPA

Anonymous at Tue, 9 Jul 2024 16:02:27 UTC No. 16274307

>>16273603
Lol geek
Btw geek doesn't imply intelligence or competency, merely implies an interest in the topic.

Anonymous at Tue, 9 Jul 2024 16:24:24 UTC No. 16274329

>>16273591
>>16273602
It's still an unsolved paradox you retards. The greeks were far smarter than modern soifaced mathematicians

Anonymous at Tue, 9 Jul 2024 16:27:57 UTC No. 16274333

>>16274329
1/inf=0

Anonymous at Tue, 9 Jul 2024 16:29:19 UTC No. 16274335

>>16274333
Doesn't solve shit

Anonymous at Tue, 9 Jul 2024 16:32:47 UTC No. 16274338

flaws of math:
>0 exists
>negative numbers exists
>rational numbers exists
>irrational numbers exists
>"imaginary" numbers exists
>(+-) infinity exists

Anonymous at Tue, 9 Jul 2024 16:36:42 UTC No. 16274345

Here's the paradox:
To overtake the tortoise, achilles has to perform infinitely many tasks
It is impossible to complete an actual infinite
Thus, achilles cannot overtake the tortoise

Anonymous at Tue, 9 Jul 2024 16:41:40 UTC No. 16274356

>>16274329
It's not yet solved because not even a paradox.

Anonymous at Tue, 9 Jul 2024 16:43:59 UTC No. 16274360

>>16274335
After accepting 1/inf=0, proving the sum of geometric sums is almost trivial.

Anonymous at Tue, 9 Jul 2024 16:45:41 UTC No. 16274363

>>16274356
>>16274360
So solve this paradox >>16274345 then

Anonymous at Tue, 9 Jul 2024 16:59:36 UTC No. 16274383

>>16274338
Imaginary numbers is one of the worst named things in math. Calling them orthogonal numbers, out of plane etc would be more correct.

Anonymous at Tue, 9 Jul 2024 17:04:43 UTC No. 16274389

>>16274383
Oh really? You think numbers are the same as lines?

Anonymous at Tue, 9 Jul 2024 17:13:21 UTC No. 16274415

>>16274363
[math] \displaystyle
\boxed{0 < p < 1} \\
p^n-1 = (p-1)(p^{n-1}+p^{n-2}+ \dots +p+1) \\
\dfrac{p^n-1}{p-1} = \sum \limits_{j=0}^{n-1}p^j \\
\displaystyle
\lim_{n \to \infty} \dfrac{p^n-1}{p-1} = \lim_{n \to \infty} \sum \limits_{j=0}^{n-1}p^j \\
\displaystyle
\dfrac{0-1}{p-1} = \sum \limits_{j=0}^{\infty}p^j \implies \dfrac{1}{1-p} = \sum \limits_{j=0}^{\infty}p^j
[/math]

Anonymous at Tue, 9 Jul 2024 18:38:58 UTC No. 16274613

>>16274389
>Are numbers on a number line in a line?

Anonymous at Tue, 9 Jul 2024 21:03:55 UTC No. 16275003

>>16274383
>out of plane
but they are in the plane nigga, what you where looking for is "out of line", which is still a very bad name for them, now as bad as imaginary, but not good either
>>16274345
https://en.wikipedia.org/wiki/Supertask

Anonymous at Tue, 9 Jul 2024 21:25:39 UTC No. 16275036

>>16275003
Orthogonal would still be correct for any number of dimensions.

Anonymous at Tue, 9 Jul 2024 22:00:35 UTC No. 16275096

>>16275036
sure