ELECTIVE 6

ELECTIVE 6

AUG. 18, 2021

​ESLR

​Through understanding the set of the Real Number System, Faithians will understand that God is relational so, they will know that God wants us to have a relationship with Him.

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​Bible verse:

​“The Lord is full of compassion and is merciful” James 5:11

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​Principle:

​God wants us to have a relationship with Him.

Open Ended

What is the biggest number or smallest number you could ever think of?

Open Ended

From which family do you belong to?

Can you describe your family?

​THE REAL NUMBER SYSTEM

​The real numbers is the set of numbers containing all of the rational numbers and all of the irrational numbers. 

The real numbers are “all the numbers” on the number line.

​THE REAL NUMBER SYSTEM INCLUDES...

• ​NATURAL NUMBERS

• ​WHOLE NUMBERS

• ​INTEGERS

• ​RATIONAL NUMBERS

• ​IRRATIONAL NUMBERS

• ​REAL NUMBERS

Fill in the Blanks

These numbers are also called as counting numbers, which of the set of the Real Number System are these numbers?

​Natural Numbers (N)

​the natural numbers are also called COUNTING NUMBERS. It starts at 1 up to the positive infinity.

​Remember that it is always positive.

Fill in the Blanks

It is a set of numbers that starts from zero and continues up to the positive infinity. What do we call this set of numbers?

​Whole Numbers (W)

Whole numbers are a set of numbers including all positive integers and 0. Whole numbers are a part of real numbers that do not include fractions, decimals, or negative numbers. Counting numbers are also considered as whole numbers.​

Open Ended

What is the difference between the Natural Numbers and the Whole Numbers?

The whole numbers include zero (0) wherein the counting numbers, it does not include zero (0).

Fill in the Blanks

This is a set of numbers that include negative, zero and positive numbers

​Integers (Z)

​An integer is a number with no decimal or fractional part, from the set of negative and positive numbers, including zero.

Multiple Select

Which of the following is included in the set of Integers?

Choose all that applies.

• positive numbers

• negative numbers

• zero

• with exponents

• with radicals

Fill in the Blanks

This set of numbers can be expressed as fractions or decimals, they are called...

​A rational number is a number that is of the form p/q where p and q are integers and q is not equal to 0. The set of rational numbers is denoted by Q.

In other words, If a number can be expressed as a fraction where both the numerator and the denominator are integers, the number is a rational number.

​Rational Numbers (Q)

Open Ended

Give some examples of a Rational Number

Fill in the Blanks

Is 0.923076923076923076923076923076... a rational number?

Fill in the Blanks

Is zero a rational number?

Multiple Choice

Which of the following is/are NOT a Rational Number?

• $$\sqrt[]{2}$$  

• $$\pi$$  

• $$\frac{2}{3}$$  

• $$3^2$$  

• $$φ$$  

​Irrational Numbers

​Irrational numbers are real numbers that cannot be represented as a simple fraction. These cannot be expressed in the form of ratio, such as p/q, where p and q are integers, q≠0. It is a contradiction of rational numbers.

Multiple Select

Which of the following is/ are part of the set of Real Numbers?

• Natural number

• Complex Numbers

• Whole Numbers

• Integers

• Rational Numbers

​Real Number System

All numbers except complex numbers are real numbers. The real number system has the following five subsets:

• Counting objects gives the set of natural numbers: N = 1, 2, 3, ...

• The set of natural numbers along with 0 represents the set of whole numbers: W = 0, 1, 2, 3, ...

• Measurement of debts, temperatures, etc., fall under the set of integers: Z = ..., -3, -2, -1, 0, 1, 2, 3, ...

• If we cut a cake into equal pieces, then we may have a piece that represents a fraction. This is an element of the set of rational numbers, (Q)

• The numbers that are square roots of positive rational numbers, cube roots of rational numbers, etc., such as ⎷2, shows the set of irrational numbers.

​How to be a part of God's family?

​We may belong to our individual families, we have to remember that as we receive and believe that Jesus died for our salvation, we are part of God's family.

​We are called as children of God.

Open Ended

What are the benefits of being part of God's family?