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This is an age-old problem that left mathematicians baffled for centuries. Question: Is it true that if a Tortoise is allowed to start a race in front of a Hare, then no matter much faster the Hare is, it will never be able to catch up with the Tortoise. Answer: No. Every time the hare reaches the tortoise's position, the tortoise would have already moved to a new position and when the hare gets to that new position, the tortoise would have gone to another new position. This will go on and on, so how can the Hare ever catch up. Below is an illustration of the scenario. For simplicity sake, take speed of the Tortoise to be 1/2 that of the Hare and the Hare is only 1 metre behind the Tortoise. Click 1st Leg: The animation shows you that when the hare reaches the 1m point the tortoise would have travelled 1/2 m forward. Click 2nd Leg: Now, the Hare travels 1/2 m to reach to the tortoise's position but by then the tortoise would have already gone 1/4 m ahead. And so on ...
Fact: We both know that this is absolute rubbish. Even if something is only slightly faster than another than the faster one will eventually be able to catch up and overtake. So what's wrong with the reasoning above. I will leave you to ponder. Answer will be posted next century. |