Can someone explain to me how Achilles won't eventually catch the tortoise? It's only a matter of time

He just needs to talk to Biden

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The point of the story is to illustrate a mathematical concept. In practical terms, you're right, he would catch up to the tortoise and pass it despite being mathematically behind, because they would eventually be so close together that his physical body would appear to overtake it.

>The point of the story is to illustrate a mathematical concept
No it’s not, it was invented to prove that reality is One

Holy shit

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he said "as though I was an English major" don't confuse the lad

The theory of relativity dictates Achilles will eventually overtake the tortoise. You were correct in the first place, zeno took into account only distance and not time

The fallacy of the story is the assumption that there isnt a minimum possible length of time and/or distance that is physically possible

Aristotle : thought zeno is confused by potential infinity and actual infinity. said the spatial world only has potential infinity, so he could resolve zeno's paradox
Bolzano : first guy who thought actual infinity can be happened in real world
Weierstrass : delicately refined the concept of limit with the basis of potential infinity
Cantor : first guy to explicitly theorize actual infinity, it is set theory
Russell : is the one who re-problemize Zeno's paradox. He thought set theory solved this problem. As naive as russell himself
Thompson : said actual infinity cause another problem called supertask. He formalized thompson's lamp
Benacerraf : claimed supertask only happened because it is only underspecified. But it is controversal that this claim be come up with every other supertask problem.
Adolf Grünbaum : condemn towards the skeptical one. thought supertask can be happened in real world, not just on logical one. is having the opposite position with William Lane Craig.
William Lane Craig(yeah. That one) : another skeptic on possibility of supertask. delicately refined Kalam cosmological argument. attempted to supplement the argument's premise by raising the strange nature of the supertask. was instrumental in making supertask argument popular again, regardless of validity.

I'm not fucking joking, it is not solved right now, it just show how strange philosophy is

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You're all wrong.
The sum to infinity of 1/2 + 1/4 + 1/8 + ... + 1/2n is 1.
Proof:

You can write the sum to n of the same series as:
Sn = (1/2)(0.5)^0 + (1/2)(0.5)^1 (1/2)(0.5)^2 + ... + (1/2)(0.5)^(n-1)

Then multiply both sides by 0.5 you get the same thing but with the first term removed and another final term added:
(0.5)Sn = (1/2)(0.5)^1 + (1/2)(0.5)^2 + ... + (1/2)(0.5)^(n-1) + (1/2)(0.5)^n

Now we take (0.5)Sn from Sn; that obviously removes everything but the unique terms in both equations:
Sn - (0.5)Sn = 1/2 - (1/2)(0.5)^n

Now factorise:
Sn(1-0.5) = Sn(0.5) = (1/2)(1-(0.5)^n)

Divide both sides by 0.5:
Sn = ((1/2)(1-(0.5)^n))/0.5

Now we change "n" to infinity, and since 0.5^n goes to 0 as n goes to infinity we get:
Sinfinity = (1/2)(1)/0.5 = (1/2)/0.5 = 1

So finally we get that Achilles crosses the whole distance, represented by 1, because this is a "convergent" sum which converges to 1.

>The sum to infinity of 1/2 + 1/4 + 1/8 + ... + 1/2n is 1.
Fuck I meant to say
THE SUM TO INFINITY OF 1/2 + 1/4 + 1/8 + ... + 1/2(0.5)^(n-1) is 1

>0.5^n goes to 0 as n goes to infinity
It approaches 0. It's not equal to 0. Likewise the sum to infinity of 1/2 + 1/4 + 1/8 + ... + 1/2n approaches 1 but is not 1.

Top kek, US elections are always good jokes.
t. scandi

That may be a good argument but I'm not exactly sure because I'm tryin gto imagine 0.5^n going to infinity and it seems it will just be 0.00 and the 0s will repeat for eternity. It's kind of weird to think about because infinity boggles the mind but you can imagine it will reach some number 0.00 and the 0s will repeat infinitely.

Tortoise moves at 1 mps
Tortoise headstart if 3 m
Achilles moves at 2 mps
Q: At what point does Achilles pass the tortoise?
A:
2t = 1t + 3 -> t = 3

The tortoise quite literally cannot outrun Achilles, no matter how far ahead it starts, Achilles will always catch up and pass it given enough TIME.

Kek

Someone has never taken a calculus course

Repeating decimal is a scam. Arithmetic is meant to be used with finite numbers and introducing infinity breaks the system. One day I'll prove that you're all wrong and then you'll be sorry.

Infinity breaks where relativity saves. Intrigued nonetheless; I once had an idea, imaginary numbers... We KNOW the answer and simply delude ourselves

ITT: The smartest people in the world can't into calculus

No joke, I’m an English major and I actually got to apply some of my basic maths knowledge when learning about Lacan and his mathemes

>desire asymptotically approaches its object
>the phallus is the square root of negative 1

And so on.

Konechna, since calculus is beyond statues, it requires LIFE

...

>Still wrong
Embarrassing

>Learning lacan
New Mexico?

How is that wrong?

>Achilles is going to get infinitely close to the tortoise
i love how this is impossible in real life and yet we still act like it can happen

Not a paradox.
Both the tortoise and Achilles move simultaneously, not one after another like a turn-based game.

You failed to temporalize.

>>Achilles is going to get infinitely close to the tortoise
>i love how this is impossible in real life and yet we still act like it can happen

You can physically touch tortoises in real life user. It's not illegal, and even if you're in bad shape you could catch up to them

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Unless that’s a technical term in calculus I’m not sure why I would need to temporalise (in my understanding this term means introduce the factor of time). Time doesn’t play a factor in the thought experiment.

This is the people that consider themselves intellectuals nowadays.

This is a variation of Zeno's Paradox. The funny thing is that you are right due to Planck's Constant.

Planck's Constant has nothing to do with this and you don't understand what Planck's Constant is anyway. The answer is basic calculus with the sum of an infinite series

>the sum of an infinite series
Which is impossible because it is infinite. Mathematics is wrong and can't describe every aspect of reality, which is discrete.

Precisely, the axioms of the thought experiment are wrong, thus you change the experiment.

>insert planck cube or planck sphere joke

>What is the form
I choose Kant for 10000

I agree that mathematics is limited in describing the physical world but mathematical objects have their own mind independent real existence and the claims mathematicians make about those objects can be true irrespective of their uselessness in describing the physical world.
Dunno why I assumed you were posting in good faith lol xD

>argue in good faith
Guess I missed the point, my faith was pure

The sum of the infinite series somehow precisely corresponds to the algebraic solution. Face it your intuition is wrong.

>I agree that mathematics is limited in describing the physical world but mathematical objects have their own mind independent real existence and the claims mathematicians make about those objects can be true irrespective of their uselessness in describing the physical world.

True and even better in this case the infinite series solution does describe the real world

Mid-race, Achilles realized he doesn't really know what to do with the turtle, he doesn't like turtle soup and dogs are better choice for petting, so he only pretends to try catching up to it for appearances sake, when in reality he keeps slowing down more and more and hoping everyone just goes home for dinner or something.

You take 2 tickets in a lottery of an infinite series of positive numbers. Both have a 100% chance to be a larger number than the other (there's an infinite amount of larger numbers than the #s on the tickets you have), therefore infinity isn't real because it's a contradiction.

>somehow
Kek the absolute state
Mathematics is a gimmick. Romans built aqueducts without 'calculus'. Even NASA relies more on trial and error method because calculations and simulations are useless

That has more to do with their chances of being larger than the other than with the infinity of the series?

The somehow was sarcastic. Math is logically rigorous and has empirical verification. Your argument against infinite sums is that you don't like them.

You can't sum a set of infinite objects

Show me infinite objects being summed, I'll wait (an infinite time)

what about the sum of all sums?

Guys maffs is useless Im traditional and metaphysical and esoteric anti-materialist. Zimble logic escapes me.

He just did.

Nonsense

Lmao mofo can't understand the difference between *calculating* an infinite series and *traversing* distances and corresponding times in a diminishing geometric series, given a finite speed.

Logically rigorous nonsense that agrees with the algebraic solution and empirical reality. I'll take that type of nonsense over your intuition.