To determine which of the numbers \(-13\), \(0\), or \(13\) is an integer but does not belong in either of the subsets of integers, we first need to identify the common subsets of integers:
- Positive Integers: These are integers greater than zero, such as \(1, 2, 3, ...\).
- Negative Integers: These are integers less than zero, such as \(-1, -2, -3, ...\).
- Zero: The integer \(0\) is neither positive nor negative.
Now let’s evaluate the given integers:
- \(-13\): This is a negative integer.
- \(0\): This is neither positive nor negative; it is in its own category.
- \(13\): This is a positive integer.
Among the integers provided (\(-13\), \(0\), and \(13\)), \(0\) is the only integer that does not belong to either the subset of positive integers or the subset of negative integers.
Therefore, the answer is \(0\).