Can you please explain Zeno’s paradox Achilles and the tortoise, well i have read about it in many websites and books but i don’t completely understand it.

The statement of Achilles and the tortoise paradox goes like this:

“A fleet-of-foot Achilles is unable to catch a plodding tortoise which has been given a head start, since during the time it takes Achilles to catch up to a given position, the tortoise has moved forward some distance.”

But the above paradoxical statement is not real. It will of course make us think and many may tend to agree with that.

A detailed explanation was found at the link below

The story tells that the tortoise argued with Achilles that, if given a head start, He will never be able to overtake him. He argued on the lines and convinced the Achilles and He agreed to the argument.

Consider a lamp, with a switch. Hit the switch once, it turns it on. Hit it again, it turns it off. Let us imagine there is a being with supernatural powers who likes to play with this lamp as follows. First, he turns it on. At the end of one minute, he turns it off. At the end of half a minute, he turns it on again. At the end of a quarter of a minute, he turns it off. In one eighth of a minute, he turns it on again. And so on, hitting the switch each time after waiting exactly one-half the time he waited before hitting it the last time. Applying the above discussion, it is easy to see that all these infinitely many time intervals add up to exactly two minutes.

QUESTION: At the end of two minutes, is the lamp on, or off?

ANOTHER QUESTION: Here the lamp started out being off. Would it have made any difference if it had started out being on?