{1,4, 9,16, 25, ...} is a set of numbers squared by natural numbers.

These two sets of figures can easily form a one-to-one correspondence. So, are there as many elements in each set? A teacher announced that there would be an exam one day in the next five days (Monday to Friday), but he told the class: "You can't know what day it is today, and you won't be informed of the exam until eight o'clock in the morning."

Can you tell me why I can't pass the exam? Elevator Paradox: In a skyscraper, there is a computer-controlled elevator that stops at every floor at the same time. However, Mr. Wang, whose office is near the top floor, said, "Whenever I want to go downstairs, I have to wait for a long time. The stopped elevator always goes upstairs and seldom goes downstairs. How strange! " Miss Li is also very dissatisfied with the elevator. She works in an office near the ground floor and goes to the restaurant on the top floor for lunch every day. She said: "whenever I want to go upstairs, the parked elevator always goes downstairs, and few of them go upstairs." Really annoying! "

What the hell is going on here? The elevator obviously stays on every floor for the same time, but why does it make people close to the top and bottom impatient? Paradox of grain heap: Obviously, 1 grain is not a heap;

If 1 millet is not a pile, then 2 millet is not a pile;

If two grains of rice are not piles, then three grains of rice are not piles;

……

If 99999 millet is not a heap, then 100000 millet is not a heap;

……

If 1 millet can't form a grain pile, two millet can't form a grain pile, three millet can't form a grain pile, and so on, no matter how many millet can't form a grain pile. This is the paradox of the valley heap that shocked the whole ancient Greece for a time.

Proceed from the real premise and use acceptable reasoning, but the conclusion is obviously wrong. Explain that the definition of "heap" lacks clear boundaries. It is different from multi-premise reasoning based on syllogism, and it forms a paradox in the continuous accumulation of one premise. There is no clear boundary between no heap and heap, and the solution is to introduce a fuzzy "class".

This is an example of the chain paradox, which is attributed to Eubulides in ancient Greece, and later skeptics denied it as knowledge. Soros means "heap" in Greek.