Integers are whole numbers that can be positive, negative, or zero. Irrational numbers are numbers that cannot be expressed as a simple fraction, meaning they cannot be represented as a ratio of two integers.
Since integers are exactly those whole numbers (like -2, -1, 0, 1, 2, etc.), they cannot be irrational. Therefore, the answer to the question of which numbers are both integers and irrational is:
none.