In mathematics, an algebraic number is a number that is a root of a non-zero polynomial in one variable with rational coefficients. Algebraic numbers include rational numbers, which are roots of polynomials with degree one, and irrational numbers, which are roots of polynomials with degree greater than one. Every real number is either rational or irrational, but many irrational numbers, such as π (pi), e, and √2, are not algebraic.
The set of all algebraic numbers is sometimes called the algebraic numbers, but this is a misnomer, as it also includes the zero polynomial (which has all algebraic numbers as roots) and all constant polynomials (whose only root is the number 0). It is possible to show that the algebraic numbers are countable.
The study of algebraic numbers is a central topic in algebra and number theory. Many properties of algebraic numbers can be deduced from the fact that they are roots of polynomials. For example, the fact that all algebraic numbers are either rational or irrational follows from the fact that the degree of a polynomial is the highest power of x that appears in the polynomial.
How do you know if a number is algebraic?
You can tell if a number is algebraic by looking at its algebraic property. Algebraic numbers have the property that they can be expressed as a root of a polynomial equation with integer coefficients. For example, the number 2 is algebraic because it satisfies the equation x^2-2=0. On the other hand, the number pi is not algebraic because it cannot be expressed as the root of any polynomial equation with integer coefficients. Is root 2 an algebraic number? Yes, root 2 is an algebraic number. In fact, it is the solution to the equation x^2-2=0. What is the set of algebraic numbers? The set of algebraic numbers is the set of all complex numbers that are roots of polynomials with integer coefficients. What is not an algebraic number? There are a few different ways to answer this question, but one way to think about it is that an algebraic number is any number that can be expressed as a root of a polynomial equation with integer coefficients. So, any number that cannot be expressed as a root of a polynomial equation with integer coefficients is not an algebraic number. Is 1 an algebraic number? Yes, 1 is an algebraic number. This is because 1 is the root of the polynomial x - 1, which has integer coefficients.