inf

Inf is commonly used as an abbreviation or symbol for infinity, a central concept in mathematics, philosophy, and computer science. While infinity is not a real number, it is used to describe unbounded quantities, limits, and the size of infinite sets. The symbol ∞ represents the idea in mathematics; the literal string "inf" is used in text and in computer languages to denote an infinity value, particularly in floating-point arithmetic.

In mathematics, infinity appears in two senses: as a value on the extended real line and as a concept describing unbounded behavior. The extended real line adds +∞ and -∞ to the real numbers, allowing limits to be described without special cases. Infimum, denoted inf S, is the greatest lower bound of a set S; it need not belong to the set. Related notions include supremum, limit, and divergence.

In computing, many programming environments represent positive and negative infinity as distinct floating-point values. In languages following IEEE 754, inf behaves as a very large magnitude value that propagates through arithmetic; for example, dividing by zero may yield inf or NaN, depending on the operands, and comparisons treat ±∞ as extreme values.

Infinity also appears in other domains, such as set theory (cardinality of the natural numbers is aleph-null), analysis (limits as a variable tends to infinity), and cosmology (conceptual discussions of the universe’s size). The term inf is typically distinguished from infimum, symbol ∞, and related terms like infinite, infinitesimal.