The notation "x | x is a real number" describes a variable x that belongs to the set of real numbers. Real numbers include all the numbers that can be found on the number line, encompassing both rational numbers (like integers and fractions) and irrational numbers (like \sqrt2 and \pi). In this context, the vertical bar "|" means "such that," indicating a condition that x must satisfy. This notation is commonly used in mathematics to define sets or to specify the properties of variables in equations and inequalities.