Positive number

Notation, sets, and examples

Different kinds of positive numbers are commonly named and collected into sets. Positive integers (1, 2, 3, ...) are a subset of the positive real numbers. The set of positive integers is often denoted Z+ or N+; a reference for sets and notation is available at integer sets. Positive rational numbers such as 1/2 and 4/3 and positive real numbers such as π are all greater than zero. Basic examples: +1, 2.5, 0.001, and √2 are positive.

Key properties

• Ordering: if a and b are positive and a < b, then b−a is positive.
• Arithmetic: the sum and product of positive numbers are positive; subtraction or division can yield nonpositive results.
• Zero: zero itself is neither positive nor negative; the nonnegative numbers include zero and the positive numbers.

When writing or displaying values, a leading plus sign is optional. In signed arithmetic and in computing contexts the presence of a plus sign can be meaningful for formatting or parsing; consult notation guides for details.

Uses and distinctions

Positive numbers are fundamental in measurement, finance (profits, credits), physics (magnitudes, directions), statistics, and many algorithms. It is useful to distinguish "positive" (greater than zero) from "nonnegative" (greater than or equal to zero). Many mathematical definitions and theorems treat positive numbers differently from zero or negative numbers; see background material at mathematical contexts and practical examples at applications.

For a compact visual reference the symbol is sometimes used in textbooks or slides to mark examples of positive values. Together these ideas form the basic conceptual framework for working with positive numbers across arithmetic, algebra and applied fields.