Are The Set Of Integers Closed Under Division

Integers: This set is closed only under addition, subtraction, and multiplication. Rational Numbers: This set is closed under addition, subtraction, multiplication, and division (with the exception of division by 0).The rationals, however, are closed under addition, subtraction, multiplication, and division. So the statement that 'the complex numbers are closed under addition' means that if you add two complex numbers together, you are guaranteed to get a complex number as the sum. There is no notion of "set open under addition", only closed. A set is closed under some operation if applying the operation on any elements of the set gives an element which is still in that set.Thus, multiplying two rational numbers produces another rational number. Rationals are closed under multiplication. Under Division: The rationals are not closed under division because of the possibility of division by zero.