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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
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What are the rules of integers?
To start with, the set of integers is a Group. This means that it is a set of elements (numbers) with a binary operation (addition) that combines any two elements in the set to form a third element. This Group, Z, satisfies four axioms: closure, associativity, identity and invertibility. that is, if x , y and z are integers, thenx + y is an integer (closure).(x + y) + z = x + (y + z) (associativity)there is an integer, denoted by 0, such that 0 + x = x + 0 = xthere is an integer, denoted by -x, such that x + (-x) = (-x) + x = 0.In addition, it is a Ring. A ring is an Abelian group (that is, addition is commutative: x + y = y + x) and it has a second binary operation (multiplication) that is defined on its elements. This second operation satisfies the axioms of closure, associativity and identity. It is also distributive over the first operation. That is,x*(y + z) = x*y + x*z
Which The following examples illustrate the commutative property of addition. 7 plus 8 plus 3 7 plus 3 plus 8 4.6 plus 11.4 11.4 plus 4.6?
5 + (-5) = 0 -1.33 + 1.33 = 0 Inverse property of addition: For real numbers, a + = 0.
What is the difference between the zero property of multiplication and the identity property of addition?
Usually, the identity of addition property is defined to be an axiom (which only specifies the existence of zero, not uniqueness), and the zero property of multiplication is a consequence of existence of zero, existence of an additive inverse, distributivity of multiplication over addition and associativity of addition. Proof of 0 * a = 0: 0 * a = (0 + 0) * a [additive identity] 0 * a = 0 * a + 0 * a [distributivity of multiplication over addition] 0 * a + (-(0 * a)) = (0 * a + 0 * a) + (-(0 * a)) [existence of additive inverse] 0 = (0 * a + 0 * a) + (-(0 * a)) [property of additive inverses] 0 = 0 * a + (0 * a + (-(0 * a))) [associativity of addition] 0 = 0 * a + 0 [property of additive inverses] 0 = 0 * a [additive identity] A similar proof works for a * 0 = 0 (with the other distributive law if commutativity of multiplication is not assumed).
Give example of closure property?
Add two positive integers and you ALWAYS have a positive integers. The positive integers are closed under addition.
Which property is shown by -6 0-6 comunitive property of addition identity property of addition distributive property or associative property of addition.?
Addition identity.
