A transcendental number is a type of real or complex number that is not a root of any non-zero polynomial equation with rational coefficients, distinguishing it from algebraic numbers. Examples include numbers like π and e, which are crucial in various fields of mathematics due to their unique properties and occurrence in natural phenomena.

Transcendental Number

transcendental number

Real Number

Complex numbers are essential in mathematics as they extend the real numbers by including the square root of negative one, defined as the imaginary unit 'i'. This allows for the solution of equations that have no real solutions, enabling progress in various fields such as engineering, physics, and applied mathematics.

complex number

non-zero polynomial equation

Rational coefficients are numbers that can be expressed as the quotient of two integers, where the denominator is not zero, and are used in algebraic expressions and equations to allow for precise manipulation and solution. They are essential in polynomial equations, enabling operations such as addition, subtraction, multiplication, and division to be performed while maintaining the rationality of the coefficients.

rational coefficients

Algebraic numbers are complex numbers that are roots of non-zero polynomial equations with rational coefficients, encompassing both rational numbers and certain irrational numbers. They form a field, which is a fundamental component in number theory and algebra, contrasting with transcendental numbers that cannot be roots of such polynomials.

Your Courses

Relevant Degrees

Your Lessons