One is infinitely cyclic decimal, such as 0.010010010001

Second, radical formulas, such as √2, √3, (√5- 1)/2, etc.

The third is the functional formula, such as: lg2, sin 1 degree, etc.

Fourth, special symbols, such as π, E, Y.

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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").

Irrational numbers can also be treated with non-terminating continued fractions.

Irrational number refers to a number that cannot be expressed as the ratio of two integers within the real number range. Simply put, an irrational number is an infinite cyclic decimal with 10 as the base, such as pi and root number two.

Rational numbers are composed of all fractions and integers, which can always be written as integers, finite decimals or infinite cyclic decimals, and can always be written as the ratio of two integers, such as 2 1/7.

Irrational numbers were first discovered by a disciple of Pythagoras.

The mathematical crisis caused by irrational numbers lasted until the second half of19th century. 1872, the German mathematician Dai Dejin started from the requirement of continuity, defined irrational numbers through the division of rational numbers, and established the theory of real numbers on a strict scientific basis, thus ending the era when irrational numbers were regarded as "irrational numbers" and the first great crisis in the history of mathematics that lasted for more than two thousand years.