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Which of the following best defines integers?

  1. All real numbers

  2. Whole numbers, including negative and zero

  3. Only positive whole numbers

  4. Numbers that cannot be expressed as fractions

The correct answer is: Whole numbers, including negative and zero

The definition of integers encompasses whole numbers and their negative counterparts, along with zero. Therefore, the option indicating that integers consist of whole numbers, including negative numbers and zero, accurately captures the complete set of integers. Integers can be represented as ..., -3, -2, -1, 0, 1, 2, 3, ..., illustrating that they include both positive and negative whole numbers as well as zero. Other options do not provide an accurate description: the option stating "all real numbers" encompasses integers, fractions, and irrational numbers, which extends beyond the scope of integers alone. The option that mentions "only positive whole numbers" is clearly limited and excludes negatives and zero, which are essential components of the integer set. Lastly, the perspective that defines integers as "numbers that cannot be expressed as fractions" inaccurately describes the nature of integers because integers can be expressed as fractions (for example, the integer 3 can be expressed as 3/1). Thus, the broader and more accurate definition is that integers include all whole numbers, both positive and negative, along with zero.