What defines an integer in mathematics?

An integer in mathematics is specifically defined as a whole number that can be either positive, negative, or zero, but crucially, it does not have any fractional or decimal portion. This means that integers are whole numbers without fractions, such as -2, 0, 3, and so on.

When considering the other options, the first choice describes numbers that include a fractional component, which directly contradicts the definition of integers. The third choice refers to numbers that include decimal points, again not applicable to integers. The fourth choice addresses the broader concept of numerical representations, which could include integers, but does not specifically define what an integer is.

Therefore, the second choice accurately captures the essence of what an integer is, making it the correct answer.