![]() ![]() There are only two morphic numbers the golden number and the plastic number, which are both irrational numbers. ![]() If a number is not an algebraic number then it is a transcendental number.Irrational numbers may or may not be algebraic.All rational numbers and integers are algebraic.Ferdinand von Lindemann proved that pi was transcendental in 1882. ![]() Charles Hermite proved that the number e was transcendental in 1873. Joseph Liouville (1809-1882) “ Liouville’s theorem” first proved the existence of transcendental numbers in 1844. There are more transcendental numbers than algebraic numbers but it’s not easy to prove a specific number is transcendental. ![]() Why? That’s beyond the scope of this numbers FAQ but this convinced us: Between any two rational numbers there will be an infinite number of irrational numbers.Ī transcendental number is a real number or an imaginary number that is not an algebraic number. There are infinitely more irrational numbers than rational numbers. Pi for example: π=3.141592653589793…Īre there more irrational numbers or more rational numbers? The decimal expansion of an irrational number never ends and never repeats. Irrational numbers are real numbers which cannot be written as a fraction.
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