Positive integers are defined as whole numbers greater than zero. However, there are several synonyms for the term which can be used interchangeably. These include natural numbers, counting numbers, and non-negative integers. Natural numbers are positive integers that are used for counting and do not include fractions, decimals, or negative numbers. Counting numbers are positive integers used in counting and ordering. Non-negative integers are whole numbers greater than or equal to zero. These synonyms can be useful in different contexts, such as in mathematics, computer science, or economics, where the term 'positive integers' might be used in a specific way.