Infinity is not a number, it is a concept that represents something that is endless or boundless. Therefore, it is not possible to perform arithmetic operations like addition, subtraction, multiplication, or division with infinity.

However, in some mathematical contexts, it is possible to define different types of infinity and perform operations with them. For example, in set theory, there are different sizes of infinity, and it is possible to compare them and perform operations with them.

In any case, the result of adding infinity to infinity is undefined or indeterminate, depending on the context.