Which of the following defines an integer?

The definition of an integer is correctly outlined as a number that can be positive, negative, or zero, while explicitly excluding fractions and decimals. Integers include all whole numbers in the positive direction (1, 2, 3, ...) as well as their negative counterparts (-1, -2, -3, ...) and zero (0). This expansive definition allows for a comprehensive understanding of integers within the number system, emphasizing that they encompass both directions along the number line without fractions.

The other options either limit the definition of integers or mischaracterize them. For example, stating that an integer can only be positive excludes negative integers and zero, while defining it as a fraction ignores the very essence of what integers represent. Therefore, the broad and inclusive definition provided makes option B the accurate characterization of integers.