Explain real numbers chapter in breif
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Answer:
A natural number is a counting number. Hence a set of natural number can be shown as N = {1, 2, 3, . .}
A whole number is all the natural numbers including 0. Therefore a set of whole numbers is W = {0, 1, 2, ..}
An integer is a set of all positive and negative whole numbers. The set of integers can be written as Z = { -4, -3, -2, -1, 0, 1, 2, . . }. The natural numbers (excluding zero) are known as positive integers. When a number gives zero on being added to its corresponding positive value is known as a negative integer. When we consider zero along with the natural numbers, we call it non-negative integers.
A rational number is any number that can be expressed in p / q form where both the numerator and denominator are integers and the value of q is positive. This includes all integers, natural numbers and rational number. Any two rational numbers has infinite rational numbers between them. The rational number can either be terminating decimal or non-terminating decimal, which can again be recurring or non-recurring in nature. There are certain operations of rational numbers that need to be accounted for. The sum of two rational numbers is a rational number. The same hold for difference and product too. This may or may not be true for division.
An irrational number is a number that cannot be expressed in p / q format. We can represent the set of irrational numbers on a number line with the help of Pythagoras theorem.
What are real numbers?
A collection of rational numbers and irrational numbers make up the set of real number. A real number can be expressed on the number line and has some specific properties. They satisfy:
The commutative law of addition. That is, when a and b are two real numbers then a + b = b + a. For example 1 + 3 = 3 + 1 = 4
The commutative law of multiplication. That is, when a and b are two real numbers then a x b = b x a. For example 1 x 3 = 3 x 1 = 3
The associative law of addition. That is, when a, b and c are three real numbers then a + (b + c) = (a + b) + c. For example 1 + (3 + 4) = (1 + 3) + 4 = 8
The associative law of multiplication. That is, when a, b and c are three real numbers then a x (b x c) = (a x b) x c. For example, 1 x (3 x 4) = (1 x 3) x 4 = 12
The law of distribution. That is, when a, b, c are three real numbers then
a x (b +c) = (a x b) + (a x c). For example 1 x (3 + 4) = (1 x 3) + (1 x 4)
= 7
There are some laws of exponents as well that is demonstrated by real numbers. They are:
ap x aq = a (p+q)
ap / aq = a(p-q)
(ap)q = apq
ap x bp = (a
Step-by-step explanation:
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