Simply put, ancient people associated numbers with the concept of distance in the real world. Some people think that any distance can be expressed as M/N, and both m and n are integers. After all, infinite cyclic decimals can be written as such fractions, so many people have confidence in this concept. It was not until later that it was discovered that the diagonal length of a square with a side length of 1 could not be described by such a number. Everyone feels very strange about this phenomenon, which leads to the reflection on the concept of logarithm.

Is infinitesimal zero? -The second mathematical crisis

Early creators of calculus, such as Newton, liked to write speed like V = LIMT-> in his works. 0 (x/t), because Newton did not give this lim t->; 0, so it was questioned a lot, for example, a knowledgeable bishop accused it of being unclear.

The Emergence of Paradox —— The Third Mathematical Crisis

Suppose a barber says, "I cut the hair of people in the village who don't cut their own hair."

Think about this sentence carefully, isn't it interesting?

Because at that time, the basic concepts of mathematics had been decided. There are many problems in using set theory to express this sentence, so a big discussion about the basis of logic and mathematics was launched.