GREATERTHAN

Greater-than, denoted by the symbol >, is a binary relation used to compare two quantities. For numbers, the statement a > b means that a is larger than b. On the real number line this places a to the right of b. In mathematics, > is a strict total order on numbers, characterized as irreflexive (no number is greater than itself), transitive (if a > b and b > c, then a > c), and total (for any distinct a and b, either a > b or b > a).

In practice, greater-than is used to express inequalities, define intervals, and describe solution sets to problems. Examples include 5 > 3 and -2 > -5. The non-strict counterpart, ≥, forms a related order relation and is often used to describe inclusive bounds. The relation > is closely linked to its opposite, <, since a > b is equivalent to b < a, and to the non-strict inequalities via trichotomy: for any a and b, exactly one of a > b, a = b, or a < b holds.

Beyond pure mathematics, greater-than appears in numerous disciplines and applications. In computer science, > is a common comparison operator that yields a boolean result used in conditional statements and loops. In programming, its behavior can vary with data types (numbers, strings, or user-defined objects) and may interact with special values such as NaN in floating-point contexts. In data analysis and statistics, order relations including > serve to rank observations and to sort data.

Overall, greater-than is a foundational relation that communicates that one quantity exceeds another, underpinning arithmetic, logic, and computational decision-making.