Whether a fraction is irrational depends on the result of division. If the result is an infinite cycle, it is rationality; If the result is infinitely acyclic, it is an irrational number, which is 22/7, that is, 22 ÷ 7 = 3.1428 571428 571. This result is an infinite cyclic decimal, so 22/7 is not an irrational number, but a rational number.

In mathematics, irrational numbers are all real numbers of irrational numbers, which are numbers composed of the ratio (or fraction) of integers. When the length of two line segments is irrational, the line segments are also described as incomparable, that is, they cannot be "measured", that is, they have no length ("measured").

The representation of irrational numbers in the position number system will not be terminated or repeated, that is, it does not contain the subsequence of numbers. For example, the decimal representation of the number π starts from 3.141592653589793, but there is no finite number that can accurately represent π, so it is not repeated.

Mathematically, a rational number is the ratio of an integer a to a positive integer b, such as 3/8. The general rule is a/b, and 0 is also a rational number. A rational number is a set of integers and fractions, and integers can also be regarded as fractions with a denominator of 1. The fractional part of a rational number is a finite or infinite cyclic number. Real numbers that are not rational numbers are called irrational numbers, that is, the fractional part of irrational numbers is infinite cyclic numbers.

Ordinary irrational number

(1) pi (π): 3.14159265358979333+0950286438+0 (infinite acyclic).

(2)e is a constant in mathematics, an infinitely acyclic decimal and a transcendental number, and its value is about 2.7 1828 (infinitely acyclic).

(3)√2,√5。 (infinite loop)

Judging whether a number is irrational depends on whether it is infinite and whether it circulates after the decimal point.

Discovery of irrational numbers

In 500 BC, there was a cow named Pythagoras. If you are a little strange to this cow, you must know the Pythagorean theorem, that is, "in a right triangle, the sum of the squares of two right angles is equal to the square of the hypotenuse."

In our country, this theorem is the famous Pythagorean theorem.

In the Pythagorean era, this theorem also had an interesting name, called "Hundred Cows Theorem". The reason is that Pythagoras was so excited when he discovered and proved this theorem. Legend has it that he killed 65,438+000 cows to sacrifice to the gods, thanking them for their inspiration.

This cow founded a school of mathematics called Pythagoras School. Don't think that this school is the same as the post-modern art school. Pythagoras school was basically a religion at that time.

For example, this school has some strange rules, such as "Don't eat beans" and "Don't stir the fire with iron". Pythagoras himself, as the "founder", called the school he founded a "cult". When he gave a lecture to the students, he stood on the altar wearing a white cassock and a golden crown.

The philosopher Heraclitus commented on him: "Pythagoras read many books and personally created wisdom, knowledge and witchcraft." 」

So what is the god that Pythagoras believes in? Don't laugh, they believe in numbers.

The order believes that integers, like atoms, constitute and describe everything in the universe. Everything in the universe can be measured by integers or the ratio of integers, and nothing else.