"Master Leibniz, isn't this just a simple math problem?" Tik asked in confusion.

Not to mention wizards like them who are proficient in mathematical Olympiads, even an apprentice can do it.

Alva and the others were also extremely disappointed. Was this the only problem that had troubled the entire Mathematical Olympiad? Was this the only problem? "Do you really think it's easy?" Leibniz looked at the people present and said regretfully. "The question is not when we can catch up, but why we can catch up."

“Zeno told me that at his speed, it would take ten seconds to reach the turtle’s starting point!

But when he arrived, the tortoise had already moved a meter. Although the distance between them was much closer, it was still a meter, so he needed to spend another tenth of a second to reach the tortoise's current position. However, the tortoise had already traveled another distance, so he had to spend one thousandth of a second to catch up with the tortoise..."

As Leibniz spoke, he stretched out his right hand and used magic to draw a line in the air as the start and end of the track. He then used red light to represent the distance Zeno had traveled, and green light to represent the distance the tortoise had traveled. The two were getting closer, but there was always a slight distance between them. No matter how small the distance was, it always existed...

Zeno seemed unable to catch up with the slow-moving tortoise in front of him despite running wildly...

Tik and the others stood there in a daze, their expressions gradually turned solemn, and soon they fell into deep thought.

This theory is easy to understand. When the wizard named Zeno was chasing the tortoise, he had to pass by the tortoise's starting point. When he reached the starting point, the tortoise had crawled forward a little further, which meant that there was a new starting point waiting for him. This theory can be repeated endlessly...

Alva thought hard and always felt that something was wrong, but he couldn't figure out what it was.

He didn't know that this was a feeling that contradicted reality and mathematical logic.

Tik was almost confused, and after a while, he suddenly reacted. "Wait, Master Leibniz, no matter what, Zeno will always catch up with the tortoise at the eleventh second, right?"

"That's the problem, my friends!" Leibniz nodded, then raised his voice a little. "If time and space are infinite and can be divided endlessly, then logically, the latecomer in the race will never be able to beat the former, because there are countless one percents between them.

This distance is infinite in a sense, after all, it can be divided into countless equal parts!"

"But since Zeno was sure to catch up with the tortoise, does that mean that in our world, space and time are not continuous, but there is a minimum scale of space and time. It is precisely because Zeno, as a latecomer, crossed this minimum scale at some point that he caught up with the tortoise..."

"Your thoughts are truly thought-provoking, Master Leibniz!" Alva let out a breath and said admiringly.

The wizards then understood that the two masters of arcane mathematics were not really arguing over a so-called racing problem. The key to the argument was whether a number could be infinitely subdivided, and what they were exploring was the question of whether the smallest scale of time and space existed.

"So, you have reached a conclusion and won the dispute, right?" Tik said happily. He admired Tik's creative thinking, which reversely deduced the smallest possible scale of time and space from a race that was bound to win! " No, because then I can't answer his second question!" Leibniz said in distress.

Is there a second question? Alva and the others suddenly felt their scalps tingling.

Leibniz stretched out his hand, and an iron arrow emerged in the void. At an extremely fast speed, it was nailed to the bookshelf beside him. Then he turned around and looked at several people and asked.

This was another question so simple that it could be answered without much thought. However, this time, Tik, Ellison and others hesitated for a long time, wondering if there might be any deeper meaning in it.

Alva on the side didn't care so much and said firmly, "Of course it's moved!"

He witnessed it with his own eyes, right in front of his eyes. Even if the other party said a lot, it couldn't change this fact! "According to what we just said, time has a minimum scale. So in every minimum scale, does this iron arrow have a definite position, and is the space it occupies the same as its volume?" Leibniz continued to ask.

Alva frowned and pondered for a long time before he said carefully, "I think so."

"So, without considering other factors, at this moment, is the arrow moving or not?" Leibniz continued.

"Of course I won't move!" Alva responded with certainty.

Tik and others also nodded. As long as they imagined that time stopped at a certain point in time, they would naturally be able to see a hovering iron arrow.

"Since this moment is motionless, what about the other moments?"

"It should... not move either?" Alva said uncertainly.

"That is to say, it is stationary at every point in time, so the arrow that is shot out is also stationary, right?" Leibniz asked finally.

"Of course..." Alva responded hesitantly, and then he was stunned. How could a flying arrow be motionless?

Tik, Ellison and others all frowned.

If Leibniz's previous statement is correct, time has a smallest scale and cannot be divided any further, then according to the logical deduction just now, the iron arrow is still at every moment, and the flying arrow cannot be in motion. After all, how can you say that something that is always still is moving?

Could it be that the sum of infinite static positions is equal to motion itself? Or that infinitely repeated static positions are motion? If Leibniz is wrong, there is no such thing as a minimum scale, time can be infinitely subdivided, and everything is continuous, then the flying arrow will naturally be in motion all the time, and the basis of this paradox will no longer exist.

But in this case, wouldn't Zeno never be able to surpass the tortoise?

Everyone present suddenly felt like they were caught in a huge vortex, wavering between the movement and stillness of the iron arrow and the paradox of whether Zeno could catch up with the tortoise. Their brains seemed to be about to explode...

Leibniz looked at Tieck and the others who were thinking hard and couldn't help but smile. These two paradoxes may seem simple, but if they were put into the 17th and 18th centuries, they would have triggered the second mathematical crisis! (End of this chapter)