Irrational number number to ratios of continuous magnitude. In his commentary on Book 10 of the "Elements", the Persian mathematician Al-Mahani (d. 874/884) examined and classified quadratic irrationals and cubic irrationals. He provided definitions for rational and irrational magnitudes, which he treated as irrational numbers. He dealt with them freely but explains them in geometric terms as follows: In contrast to Euclid's concept of magnitudes as lines, Al-Mahani considered integers and fractions as rational magnitudes, and square roots and cube roots as irrational magnitudes. He also introduced an arithmetical approach to the concept of irrationality, as he attributes the following to irrational
Irrational number 1 = 0, and this latter polynomial has no rational roots (the only candidates to check are ±1, and "x", being greater than 1, is neither of these), so "x" is an irrational algebraic number. Because the algebraic numbers form a subfield of the real numbers, many irrational real numbers can be constructed by combining transcendental and algebraic numbers. For example, 3 + 2, + and "e" are irrational (and even transcendental). The decimal expansion of an irrational number never repeats or terminates (the latter being equivalent to repeating zeroes), unlike any rational number. The same is true for binary,