ELECTIVE 6

​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.

​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.

• ​NATURAL NUMBERS

• ​WHOLE NUMBERS

• ​INTEGERS

• ​RATIONAL NUMBERS

• ​IRRATIONAL NUMBERS

• ​REAL NUMBERS

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

​Remember that it is always positive.

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.​

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

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

​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.

​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.

​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.

​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.