"In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 feet. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 feet, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, for example 10 feet. It will then take Achilles some further period of time to run that distance, in which period the tortoise will advance farther; and then another period of time to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise." -Wikipedia

This seems like a very interesting topic.

If infinity can not be reached, he can not pass.

Or maybe infinity is reached, and he is able to overtake.

What is the solution? How can Achilles overtake the Tortoise?

he should just keep on going?

But then the Tortoise moves ahead.

well then he could never catch him

But he is going faster.

It is obvious he will pass since he goes faster.

^but i thought you said he can never pass the tortoise?

To solve assign some numbers, then you will see exactly when he will pass the tortoise. To look at this in this light is looking at it incorrectly. Especially since infinity cannot be attained by something finite, like distance.

Infinity is unreachable. So he can not pass.

Yet he is faster, so he can pass.

That's why it is called a paradox brute.

yeah i get it now

This paradox shows that Mathematics is abstract and can´t always be taken to a literal context in real life.

There´s this joke - One engineer, one physicist and one mathematician are called to calculate how much water would be needed to put out a large fire.

After 5 hours, the engineer says: "You need 10,000 gallons of water".
After 12 hours later, the physicist says: "You need 9,932.56 gallons of water".
After 3 days, the mathematician says: "Your problem has an answer and it is unique"

Got it?