Irrational number, also known as infinite acyclic decimal, cannot be written as the ratio of two integers. If written in decimal form, there are infinitely many digits after the decimal point, which will not cycle. Common irrational numbers include the square root, π and E (the latter two are transcendental numbers) of incomplete square numbers. Another feature of irrational numbers is the expression of infinite connected fractions. Irrational numbers were first discovered by a disciple of Pythagoras.

0 is not an irrational number, 0 is a rational number. So irrational numbers include positive irrational numbers and negative irrational numbers. Does not contain 0.

Extended data:

0 is an integer between-1 and 1. Is the smallest natural number and also a rational number. 0 is neither positive nor negative, but the dividing point between positive and negative numbers. 0 has no reciprocal, the reciprocal of 0 is 0, the absolute value of 0 is 0, the square root of 0 is 0, the cube root of 0 is 0, 0 times any number equals 0, and the power of 0 of any number except 0 equals 1. 0 cannot appear as a denominator, and all multiples of 0 are 0. 0 cannot be used as a divisor.

The discovery of irrational numbers:

In 500 BC, hippasus, a disciple of Pythagoras School, discovered an amazing fact: the diagonal of a square is incommensurable with the length of one side (if the side length of a square is 1, the length of the diagonal is not a rational number), which is quite different from Pythagoras School's philosophy of "everything is a number" (referring to a rational number).

This discovery frightened the leaders of the school, thinking that it would shake their dominant position in the academic world, so they tried their best to stop the spread of this truth, and Herbesos was forced into exile. Unfortunately, he met his disciples on a seagoing ship. Was brutally thrown into the water by Pisces disciples and killed. Thus began the history of science, but it was a tragedy.