PositiveInteger

A positive integer is a whole number that is greater than zero. In mathematics, the set of positive integers is commonly denoted by the symbol $\mathbb{Z}^{+}$. This set includes the numbers 1, 2, 3, 4, and so on, extending infinitely. Positive integers are fundamental building blocks in number theory and are used extensively in arithmetic, algebra, and various branches of mathematics.

The concept of positive integers is closely related to the concept of natural numbers. While the definition of natural numbers can vary, sometimes including zero and sometimes excluding it, positive integers exclusively refer to the numbers greater than zero. This distinction is important in contexts where zero is treated separately. For example, in set theory, the natural numbers might be defined as $\{0, 1, 2, \dots\}$, while positive integers would be $\{1, 2, 3, \dots\}$.

Properties of positive integers include their closure under addition and multiplication, meaning that the sum or product of any two positive integers is also a positive integer. They also possess properties related to ordering, such as being either even or odd, and being either prime or composite (with the exception of the number 1, which is neither). The study of their properties, such as divisibility and prime factorization, forms a significant part of number theory.