Three paradoxes in the world: Pythagoras paradox, Becquerel paradox and Russell paradox. Paradox usually refers to such a proposition. According to the generally accepted logical reasoning method, two opposite conclusions can be drawn. The form is: If event A occurs, it is not; if it is not, it is. ..

1, Pythagoras paradox

In the 5th century BC, the discovery of incommensurable measures led to the Pythagorean paradox. At that time, the Pythagorean school attached importance to the study of the invariable factors in nature and society, and called geometry, arithmetic, astronomy and music "four arts", in which it pursued the harmony and law of the universe.

They think that everything in the universe can be summed up as an integer or a ratio of integers. A great contribution of the Pythagorean school is to prove the Pythagorean theorem, but it is also found that the hypotenuse of some right-angled triangles cannot be expressed as integers or the ratio of integers (incommensurability), such as right-angled triangles with all right-angled sides of 1.

2. Becquerel paradox.

In the history of mathematics, the Becquerel problem is called "Becquerel Paradox". Generally speaking, Becker's paradox can be expressed as "whether infinitesimal is zero": for the practical application of infinitesimal at that time, it must be both zero and non-zero. But as far as formal logic is concerned, this is undoubtedly a contradiction.

3. Russell paradox

Russell Paradox: Let the property P(x) mean that "x does not belong to a". Now suppose that a class A is determined by the property p-that is, "A={x|x? A}. Then the question comes: Is it true that A belongs to A?

First of all, if A belongs to A, then A is an element of A, then A has the property P, which shows that A does not belong to A; Secondly, if A does not belong to A, that is to say, A has the property P, and A consists of all classes with the property P, then A belongs to A. ..