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.
To any set that contains it! It belongs to {5.385164807}, or {45, sqrt(2), pi, 5.385164807, -3/7}, or all numbers between 4 and 53, or rational numbers, or real numbers, or complex numbers, etc.
Any set that contains -1.2, whether finite or infinite. For example, the set consisting of only -1.2 ie {-1.2}, the set consisting of -1.2 and 5 = {-1.2,5}, the set consisting of -1.2 and 3 and sqrt(17) = {-1.2,3,sqrt(17)}, and so on.
It belongs to many many subsets including: {sqrt(13)}, The set of square roots of integers The set of square roots of primes The set of square roots of numbers between 12 and 27 {3, -9, sqrt(13)} The set of irrational numbers The set of real numbers
To any set that contains it! It belongs to {7.5}, or {7.5, sqrt(2), pi, -3/7}, or {7.5, bananas, France, cold} or multiples of 2.5, or halves of odd integers, or rational numbers, or real numbers, or complex numbers, etc.
fractions
Whole numbers, composite numbers, odd numbers, numbers divisible by 3, and many more.
The Rationals, the set {1, 3 , 5.86, sqrt(59), -2/3, pi2}, the reals numbers, numbers between 5 and 6, etc.
Natural (counting) numbers; integers; rational numbers; real numbers; complex numbers. And any other set that you choose to define, that happens to include the number 4 - for example, the set of square numbers, or even numbers, the set of the numbers {3, 4, 5, 7, 14, 48}, etc, the set of numbers containing the letter o in their English name.
Natural numbers.
Any set of numbers that contain them! For example, they belong to the set {10, 11} or {10, 11, sqrt(2), pi, -3/7}, or {10, 11, bananas, France, cold} or all whole numbers between 3 and 53, or counting numbers, or integers, or rational numbers, or real numbers, or complex numbers, etc.
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.
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.
It belongs to any set that contains it: The set of numbers between 3 and 4, The set containing only the number 3.1414 repeating, The set containing 1, 3.1414 (r) , and sqrt(37) The set of rational numbers, The set of real numbers, etc
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
To any set that contains it! It belongs to {5.385164807}, or {45, sqrt(2), pi, 5.385164807, -3/7}, or all numbers between 4 and 53, or rational numbers, or real numbers, or complex numbers, etc.
Any set that contains -1.2, whether finite or infinite. For example, the set consisting of only -1.2 ie {-1.2}, the set consisting of -1.2 and 5 = {-1.2,5}, the set consisting of -1.2 and 3 and sqrt(17) = {-1.2,3,sqrt(17)}, and so on.