math 11.pptx

math 11.pptx

• 1.
  Real Numbers Real numberis any number that can be found in the real world. We find numbers everywhere around us. Natural numbers are used for counting objects, rational numbers are used for representing fractions, irrational numbers are used for calculating the square root of a number, integers for measuring temperature, and so on. These different types of numbers make a collection of real numbers. In this lesson, let us learn all about what are real numbers, the subsets of real numbers along with real numbers examples.
• 2.
  Set of RealNumbers •Any number that we can think of, except complex numbers, is a real number. For example, 3, 0, 1.5, 3/2, √5, and so on are real numbers.
• 3.
  Definition of RealNumbers •Real numbers include rational numbers like positive and negative integers, fractions, and irrational numbers. Now, which numbers are not real numbers? The numbers that are neither rational nor irrational are non-real numbers, like, √-1, 2 + 3i, and -i. These numbers include the set of complex numbers, C.
• 4.
  Set of RealNumbers •The set of real numbers, which is denoted by R, is the union of the set of rational numbers (Q) and the set of irrational numbers (Ǭ). So, we can write the set of real numbers as, R = Q U Ǭ •. This indicates that real numbers include natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Observe the following table to understand this better. The table shows the sets of numbers that come under real numbers.
• 6.
  List of RealNumbers •The list of real numbers is endless because it includes all kinds of numbers like whole, natural, integers, rational, and irrational numbers. Since it includes integers it has negative numbers too. So, there is no specific number from which the list of real numbers starts or ends. It goes to infinity towards both sides of the number line.
• 7.
  Rational Numbers •Any numberwhich can be defined in the form of a fraction p/q is called a rational number. The numerator in the fraction is represented as 'p' and the denominator as 'q', where 'q' is not equal to zero. A rational number can be a natural number, a whole number, a decimal, or an integer. For example, 1/2, -2/3, 0.5, 0.333 are rational numbers.
• 8.
  Irrational Numbers •Irrational numbersare the set of real numbers that cannot be expressed in the form of a fraction p/q where 'p' and 'q' are integers and the denominator 'q' is not equal to zero (q≠0.). For example, π (pi) is an irrational number. π = 3.14159265...In this case, the decimal value never ends at any point. Therefore, numbers like √2, -√7, and so on are irrational numbers.
• 9.
  Symbol of RealNumbers • Real numbers are represented by the symbol R. Here is a list of the symbols of the other types of numbers. • N - Natural numbers • W - Whole numbers • Z - Integers • Q - Rational numbers • Ǭ - Irrational numbers