Subsets of Real Numbers

Introduction

In real life, what does it mean to be real?

This is a technological age where the development of different apps is active. Social media applications allow different persons to connect virtually. As research shows, the real connection, the true empathy is missing during these connections and even during physical conversations. We may be physically present, but we are absent because of what we do such as browsing our phones instead of taking time to converse with each other.

The proper way of using these numbers is the most reasonable and practical way to provide value and meaning. In the market, when we buy meat, we prefer to use fractions or mixed numbers, for instance, 1/2 kilo of chicken or 3 1/4 kilos of beef, but in paying for the products, we use money which is in decimal form with two decimal places.

 

Name

Description

Examples

Natural Numbers (N)

These numbers are used for counting, also known as counting numbers.

{1, 2, 3, 4, 5...}

Whole Numbers (W)

These numbers are formed by adding zero to the set of natural numbers.

{0, 1, 2, 3, 4, 5...}

Integers (Z)

They are formed by adding the negatives of the natural numbers to the set of whole numbers.

{... -4, -3, -2, -1, 0, 1, 2, 3, 4...}

Rational Numbers (Q)

The set of all numbers which can be expressed in the form a/b, where a and b are integers, b is not equal to 0.

5.34, 67, 0.131313..., ¾,

9

Irrational Numbers (Q’)

The set of numbers whose decimal representations are neither terminating nor repeating. These numbers cannot be expressed as a quotient of integers.

√2, 4.626578…, e and 𝜋
Task

At the end of the lesson, the learner should be able to:

  1. Describe and illustrate the real number system.
  2. Identify the subsets of real numbers.
  3. Recall irrational and rational numbers
  4. Give examples of the subsets of real numbers
Process

1. We are going to divide the class into three groups

2. Each group must have its own leader.

3. You will pick from the given numbers (1 to 9)

4. Each number represents a question and you need to answer the question in the number you’ve picked.

5. You only have 30 seconds to answer the question.

 

 

1. e Is it rational or irrational?

2. -16.28 Is it rational or irrational?

3. Name the subset(s) of numbers to which each number belongs.   - 9

4. Name the subset(s) of numbers to which each number belongs.   3

5. Name the subset(s) of numbers to which each number belongs.   81

6. TRUE or FALSE All whole numbers are integers

7. TRUE or FALSE Some fractions are irrational numbers.

8. TRUE or FALSE Every rational number is a decimal.

9. TRUE or FALSE Zero is a counting number

10. TRUE or FALSE Set A = {0, 1, 2, 3, 4, …} is the set of whole numbers.

11. 2/5 is it rational or irrational?

Evaluation

1. Irrational

2. Rational

3. Integer, Rational, Real

4. Irrational, Real

5. Natural, Whole, Integer, Rational, Real

6. True

7. True

8. False

9. False

10. True

11. Rational

Conclusion

Real numbers are the type of numbers that we use in our everyday life. They are called real numbers because they are not imaginary. Real Number System is a system which consists of all numbers; rational, irrational, integers, whole, counting and etc.