ℝ^n, pronounced "R to the n," represents an n-dimensional space where each point is defined by n real numbers. For example, in ℝ^2, each point is represented by a pair of coordinates (x, y), while in ℝ^3, points are represented by three coordinates (x, y, z). This mathematical concept is fundamental in various fields, including geometry, physics, and computer science. The notation ℝ^n is used to describe the set of all possible n-tuples of real numbers. It allows for the generalization of concepts like distance, angles, and volume in higher dimensions. This framework is essential for understanding vector spaces and linear algebra, where operations on vectors in ℝ^n are performed.