The mathematically correct answer is: any set that contains it. For example, it belongs to the set of all numbers between -3 and +2, the set {0, -3, 8/13, sqrt(97), pi}, the set {0}, the set of the roots of x3 - x2 + x = 0, the set of all integers, the set of all rational numbers, the set of all real numbers, the set of all complex numbers.
A set of numbers is considered to be closed if and only if you take any 2 numbers and perform an operation on them, the answer will belong to the same set as the original numbers, than the set is closed under that operation. If you add any 2 real numbers, your answer will be a real number, so the real number set is closed under addition. If you divide any 2 whole numbers, your answer could be a repeating decimal, which is not a whole number, and is therefore not closed. As for 0 and 3, the most specific set they belong to is the whole numbers (0, 1, 2, 3...) If you add 0 and 3, your answer is 3, which is also a whole number. Therefore, yes 0 and 3 are closed under addition
It belongs to the set of prime numbers
Rational and Real numbers
To any set that contains it! It belongs to {0}, or {45, 0, sqrt(2), pi, -3/7}, or {0, bananas, France, cold} or all whole numbers between -43 and 53, or multiples of 5, or integers, or rational numbers, or real numbers, or complex numbers, etc.
Its an imperial numberIts belong to rational, whole, and integars.
The set of numbers which 3 does not belong is the set of even numbers.
The mathematically correct answer is: any set that contains it. For example, it belongs to the set of all numbers between -3 and +2, the set {0, -3, 8/13, sqrt(97), pi}, the set {0}, the set of the roots of x3 - x2 + x = 0, the set of all integers, the set of all rational numbers, the set of all real numbers, the set of all complex numbers.
A set is just a way of describing numbers, and numbers can be described in more than one way. If set A is (for example) all positive prime numbers, and set B is all numbers between 0 and 10, then there are some numbers (2, 3, 5, and 7) that could belong to both sets.
10 belongs to the set "natural numbers", but it can also belong to whole numbers, and rational numbers
Infinitely many sets: they belong to the set {0, 2, 4, 5, 7, 9}, and to {0, 2, 4, 5, 7, 9, 92} and {0, 2, 3, 4, 5, 7, 9} and {0, 2, 4, 5, 5.35, 7, 9} and {0, 2, 4, 5, 7, sqrt(53), 9} and N0, the set of Natural number including 0, Z, the set of integers, Q, the set of rational numbers, R, the set of real numbers, C, the set of complex numbers as well as any superset of these sets.
Counting numbers
Irrational numbers.
The set of even numbers
A set of numbers is considered to be closed if and only if you take any 2 numbers and perform an operation on them, the answer will belong to the same set as the original numbers, than the set is closed under that operation. If you add any 2 real numbers, your answer will be a real number, so the real number set is closed under addition. If you divide any 2 whole numbers, your answer could be a repeating decimal, which is not a whole number, and is therefore not closed. As for 0 and 3, the most specific set they belong to is the whole numbers (0, 1, 2, 3...) If you add 0 and 3, your answer is 3, which is also a whole number. Therefore, yes 0 and 3 are closed under addition
It belongs to the set of prime numbers
Rational and Real numbers