xeno's paradox?

[Anonymous No.8838325]

Achilles can overtake the tortoise at time > Headstart / (Achilles speed - Tortoise speed).

Let A = Achilles, O = Tortoise, H = Headstart distance. Assume Achilles runs at speed s and the tortoise at half that.

[math]x_{A} = st[/math]
[math]x_{O} = \frac{1}{2}st+H[/math]

Achilles meets the tortoise when [math]x_{A} = x_{O}[/math]
[math]st = \frac{1}{2}st+H[/math]
[math]t = \frac{H}{s(1 - \frac{1}{2})}[/math]
[math]t = \frac{2H}{s}[/math]

After 2H/s, Achilles strictly goes faster than the tortoise and overtakes the tortoise.

[Anonymous No.8838396]

I like Hofstadter's sum-of-the-infinite-series (1 = 1/2 + 1/4 + 1/8 + . . .) explanation better, but then again I'm a math brainlet.

Good job, anon, I'm proud of you.

[Anonymous No.8838590]

Just write 2 equations of motion and solve for when they meet

[Anonymous No.8838689]

>>8838325
>Achilles meets the tortoise when [math]x_A = x_O[/math]
Isn't the whole point of the paradox to refute the claim that Achilles never meets the tortoise?
If you have to assume what you need to prove, you're guilty of circular reasoning.

[Anonymous No.8838768]

>>8838689
The runner never meets the tortoise because the runner never moves, but that means the tortoise never moves either. So the paradox is that he described a still photo before cameras were invented

[Anonymous No.8838788]

>>8838325
Xeno was well known to be the first autist.

[Anonymous No.8838811]

>>8838325

[Anonymous No.8839236]

>>8838788
My sides

[Anonymous No.8839252]

>>8838325
The point is that in order to travel the distance between him and the turtle, he has to travel half the distance between him and the turtle. To travel the half distance, he needs to travel half of that distance first etc...

Obviously he can overtake the turtle but infinitesimals and infinity in general was the realm of the gods which mortals had no business in so they never developed calculus.