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Q: Why is it subtraction and division are not included in the properties of each numbers?

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Whole numbers subtraction: YesDivision integers: No.

Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.

There is no commutative property in subtraction or division because the order of the numbers cannot be change. This means that when multiplying or adding it does not matter the order of the numbers because the answer comes out the same.

Subtraction is definitely an operation defined on real numbers. I'm guessing you are actually asking why subtraction is not included as a commutative operation, this is because a-b is not always equal to b-a.

For the specific case of whole numbers, you can consider multiplication to be repeated addition; and division to be repeated subtraction (see how often you can subtract something).

Not by itself. A mathematical operation has properties in the context of a set over which it is defined. It is possible to have a set over which properties are not valid.Having said that, the set of rational numbers is closed under subtraction, as is the set of real numbers or complex numbers.Multiplication is distributive over subtraction.

They are whole numbers used in division, multiplication, addition and subtraction.

They are addition, subtraction, division and multiplication

An operation on a series of numbers is when you use amongst others addition, subtraction, multiplication and division. Mathematics decided the order of operations is to work out the sums in the brackets first, then exponents, then multiplications and division and finally addition and subtraction.

parentheses, exponents, multiplication, division, addition, and subtraction.

addition means when you add two or more numbers together.+ subtraction means you subtract two or more numbers together.- multiplication means when you mutiply two one, or more digit numbers together.x division means when you divide two numbers together./

They are closed under all except that division by zero is not defined.

The answer depends on the operation that you are thinking of: addition, subtraction, multiplication, division, etc.

For addition, subtraction, division and multiplication with other fractions

Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.

They are all numbers and obey the same rules for addition, subtraction, multiplication, division, exponentiation etc.

Arithmetic is the process of applying the four basic operations: addition, subtraction, multiplication and division to numbers.

The set of rational numbers is closed under all 4 basic operations.

You can have counting number in multiplication and addition. All integers are in multiplication, addition and subtraction. All rational numbers are in all four. Real numbers, complex numbers and other larger sets are consistent with the four operations.

You can give hundreds of examples, but a single counterexample shows that natural numbers are NOT closed under subtraction or division. For example, 1 - 2 is NOT a natural number, and 1 / 2 is NOT a natural number.

"Factor" is normally applied to multiplication and division, not addition and subtraction, but the analogues in addition would be the numbers being added.

Different sets of numbers have different properties. For example,The set of counting numbers is closed under addition but not under subtraction.The set of integers is closed under addition, subtraction and multiplication but not under division.Rational numbers are closed under all four basic operations of arithmetic, but not for square roots.A set S is "closed" with respect to operation # if whenever x and y are any two elements of S, then x#y is also in S. y = 0 is excluded for division.So, the answer depends on what you mean by "number".

Yes. In general, the set of rational numbers is closed under addition, subtraction, and multiplication; and the set of rational numbers without zero is closed under division.

Yes. The set of real numbers is closed under addition, subtraction, multiplication. The set of real numbers without zero is closed under division.

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