real number
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Add two positive integers and you ALWAYS have a positive integers. The positive integers are closed under addition.
The intersection of integers and rational numbers is the set of integers. Integers are whole numbers that can be positive, negative, or zero, while rational numbers are numbers that can be expressed as a ratio of two integers. Since all integers can be expressed as a ratio of the integer itself and 1, they are a subset of rational numbers, making their intersection the set of integers.
There is none
Because that is the definition of irrational numbers: They are the numbers that cannot be written as a ratio of two integers! A fraction is a ratio of two integers.
Can be an integer, a rational number or undefined.