Don't answer with PI or stuff like that. I would like to know the formal definition.
2006-08-07 12:05:58 · 6 answers · asked by Blues Man 2 in Science & Mathematics ➔ Mathematics
Usually, the definition is done the other way around:
An algebraic number is a root of a polynomial with integer coefficients.
For example, 2/3 is agebraic because it is a root of 3x-2, sqrt(2) is algebraic because it is a root of x^2 -2, etc. The complex number i is algebraic because it is a root of x^2 +1.
A transcenental number is then a complex number which is not algebraic.
It should be pointed out that not every algebraic number can be written interms of nested radicals as another poster claimed. In fact, there are fifth degree polynomials whose roots cannot be so written. This is related to the famous problem of solvability of polynomails by radicals.
2006-08-07 13:16:24 · answer #1 · answered by mathematician 7 · 1⤊ 0⤋
A transcendental number is a number that cannot be computed from an algebraic equation. Transcendental numbers are the sum of an infinite converging series (like 1/2 + 1/3 + 1/4 + 1/5 and so on to infinity).
2006-08-07 19:11:51 · answer #2 · answered by stevewbcanada 6 · 0⤊ 0⤋
It is any number which is not the solution to any algebraic equation with rational coefficients, or coefficients which are in a finite algebraic extension of the rationals. Therefore it cannot be a rational number (because all of these are solutions to linear equations). It cannot be any finite root or finitely nested root--for these can always be finitely squared out or whatever and turned into one of the forbidden types. It is what's left of the real numbers after you've taken out the rationals and the finitely nested surds.
2006-08-07 19:17:10 · answer #3 · answered by Benjamin N 4 · 0⤊ 0⤋
A transcendental number is a (possibly complex) number that is not the root of any integer polynomial, meaning that it is not an algebraic number of any degree. Every real transcendental number must also be irrational, since a rational number is, by definition, an algebraic number of degree one.
2006-08-07 19:12:58 · answer #4 · answered by Scottie0210 2 · 0⤊ 0⤋
The defination of a transcendentral number
Click on the URL below for additional information
en.wikipedia.org/wiki/Transcendental_number
2006-08-07 19:24:24 · answer #5 · answered by SAMUEL D 7 · 0⤊ 0⤋
They are complex numbers which cannot be used to solve a non-zero algebraic equation.
2006-08-07 19:14:32 · answer #6 · answered by Anonymous · 0⤊ 0⤋