Real Number Examples Real Number Examples Form the above description of real numbers we can say that real numbers are the combination of several parts of the number system. That’s why we can write Real Numbers Definition as: real numbers can be called as superset of all numbers (except the complex numbers). In the set representation, we can say that the real numbers can be represented as R. According to the Real Numbers Definition, all numbers (except complex numbers) of number system can be considered as a subset of real numbers. Here we are discussing about the basic properties of real numbers. A real number may be either a positive or a negative, algebraic or transcended , irrational or rational or zero numeral. Real numbers can also be represented in the form of decimal number representation like 56.4565679812. In a more understandable language, we can say that “any type of the numbers that are exist in the real world and available for use are known as real numbers”.
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In the real world we perform the various operations with the real numbers like addition , subtraction , division and multiplication . With these operations we use the several types of properties to solve the various types of difficult questions. Here are some properties of real numbers: 1) Commutative properties by addition It says for real numbers a and b,
a+b=b+a
2) Commutative properties by multiplication It says for real numbers a and b, a * b = b * a 3) Associative property by addition It says for real numbers a , b and c that, a + ( b + c ) = ( a + b ) + c 4) Associative property by multiplication It says for real numbers a , b and c that, a * ( b * c ) = ( a * b ) * c 5) Inverse property by addition It says for real number a that, a + ( - a ) = 0 6) Inverse property by multiplication It says for real number a that, a * 1 / a = 0 7) Distributive property of real numbers
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It says for real numbers a , c and c that, a * ( b + c ) = ab + ac Properties of real numbers: 1) Commutative property by addition: In this we represent the addition of two numbers. Like x +y=y+x 2) Commutative property by multiplication: In this property the operation of multiplication are performed on the given variable. For example: x * y = y * x 3) Associative property by addition: In this we want to indicate that addition of three variables by changing brackets is not affected. For example: x + (y + z) = (x + y) + z 4) Associative property by multiplication: This property of real number represents that when we multiply the three real numbers by changing the brackets position then it does not make any effect in the final output. For example: ( x * y ) * z = x * ( y * z ) 5) Inverse of addition property or additive inverse property: In this property we want to say that the sum of any real number with its opposite value (means either in negative or positive value of given number) gives the result as zero. For example: x + ( - x ) = 0 6) Inverse of multiplication property or multiplicative inverse property: In this property we want to say that the multiplication of any real number with its reciprocal value (means either in fraction or opposite of fraction) gives the result as zero. Here the value of the variable must not be equal to 0. For example: x * 1 / x = 0.
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