An algebraic set is a collection of points in a space that satisfy a set of polynomial equations. These points can be represented in various dimensions, such as in two-dimensional or three-dimensional space. Algebraic sets are fundamental in the field of algebraic geometry, where they help in understanding the solutions to polynomial equations. In more technical terms, an algebraic set can be defined as the zero set of a collection of polynomials. For example, the set of all points (x, y) that satisfy the equation x^2 + y^2 = 1 forms a circle, which is an algebraic set in Euclidean space.