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The basic operations are addition (+), subtraction (-), multilpication (*) and division (/).

But there are many others, for example, powers and roots, trigonometric functions, exponents and logarithms.

Q: What is operation on real numbers?

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The set of real numbers is closed under addition, subtraction, multiplication, and division (except that you cannot divide by zero). By closed, this means that if the two numbers in the operation are both real numbers, the result of the operation will always be a real number. Dividing by zero is undefined (for all practical purposes)

Real numbers are commutative (if that is what the question means) under addition. Subtraction is a binary operation defined so that it is not commutative.

Division, since you can't divide by zero.

Yes, the complex numbers, as well as the real numbers which are a subset of the complex numbers, form groups under addition.

rules of operation sign of numbers

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No. Negative numbers are real but their square roots are not.

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.

The answer depends on the operation under consideration.

The set of real numbers is closed under addition, subtraction, multiplication, and division (except that you cannot divide by zero). By closed, this means that if the two numbers in the operation are both real numbers, the result of the operation will always be a real number. Dividing by zero is undefined (for all practical purposes)

For the set of real numbers, R, a binary operation is a function from R X R into R, where R X R is the x-y plane. A binary operation is commutative if the value returned by the operation is the same regardless of the order of the operands. For real numbers the two most basic commutative binary operations are addition and multiplication and they can be expressed in the following way:If a and b are any two real numbers then a + b = b + a (addition is commutative) and ab = ba ( multiplication is commutative).

Real numbers are commutative (if that is what the question means) under addition. Subtraction is a binary operation defined so that it is not commutative.

Division by zero and square root of negatve number

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Division, since you can't divide by zero.

Yes, the complex numbers, as well as the real numbers which are a subset of the complex numbers, form groups under addition.

rules of operation sign of numbers

The set of integers, rational numbers, real numbers, complex numbers are some of the sets. Also, many of their subsets: for example, all numbers divisible by 3.