By definition, integers are whole numbers that can be positive, negative, or zero, while irrational numbers are numbers that cannot be expressed as a fraction of two integers and have non-repeating, non-terminating decimal expansions.
Since integers are rational numbers (they can be expressed as a fraction, for example, \( n = \frac{n}{1} \) where \( n \) is an integer), there are no numbers that are both integers and irrational numbers.
Therefore, the answer is that there are no numbers that are both integers and irrational numbers.