greaterthanorequalto

Greater than or equal to is a binary relation used to compare two values. It indicates that the first value is either greater than the second or exactly equal to it.

Notation and reading: In mathematical notation, the relation is written as x ≥ y. It is read “x is greater than or equal to y” and is the non-strict version of the greater-than relation. It holds when x > y or x = y.

Properties: For any element a, a ≥ a (reflexivity). If a ≥ b and b ≥ c, then a ≥ c (transitivity). If a ≥ b and b ≥ a, then a = b (antisymmetry). On the real numbers, ≥ defines a total order, meaning any two numbers are comparable. In higher dimensions, ≥ is often defined componentwise (a ≥ b if every component a_i ≥ b_i), which yields a partial order rather than a total one.

Examples: 5 ≥ 3 is true; 3 ≥ 5 is false; 4 ≥ 4 is true. In programming languages, the operator ≥ is a common comparison operator used in conditional statements and loops.

Applications: The symbol is used extensively in mathematics to express inequalities, in optimization and linear programming to constrain variables, in statistics to order data, and in computer algorithms to implement thresholds and decision criteria. It provides a concise way to describe “not smaller than” relationships in a wide range of contexts.