To determine which numbers in the given set are integers, let's examine each one:
1. -4: This number is an integer because it is a whole number without any fractional or decimal component.
2. 0: This is also an integer, as it is a whole number and is explicitly defined as such in the set of integers.
3. [tex]\(\frac{4}{5}\)[/tex] (or 0.8): This is not an integer because it is a fraction and has a decimal component.
4. [tex]\(0.\overline{4}\)[/tex] (or 0.4444...): This is not an integer because it is a repeating decimal and not a whole number.
5. [tex]\(\sqrt{5}\)[/tex] (or the square root of 5): This is not an integer because the square root of 5 is an irrational number, approximately equal to 2.2360, and it has a non-terminating, non-repeating decimal portion.
6. [tex]\(\pi\)[/tex] (or pi, approximately 3.14159): This is not an integer because π is an irrational number and has a non-terminating, non-repeating decimal expansion.
After analyzing each number in the set, we conclude that the integers in the given set are:
- -4
- 0
Thus, the integers in the set are:
[tex]\[
\{-4, 0\}
\][/tex]
