Introduction: Real Numbers - How deep is deep?

Class Discussion:

What is the distance between the two extremes (in metres)?

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You may want to click at the hyperlink to find out more about the "Challenger Deep".
Source: http://www.deepseachallenge.com/the-expedition/mariana-trench/

Quick Glimpse: The Number System

Below is a very much simplified representation of the various number families and their relationships. We will discuss further when we start the topic on Real Numbers.

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Broadly...
The relationship between the numbers system is as follows:

Amongst the 4 types of numbers:

• NATURAL NUMBERS is the smallest of all - starts from 1, followed by 2, 3, 4, 5, ... basically, it's positive integers
• INTEGERS is made up by negative integers (-1, -2, -3, .... ), zero (0) and positive integers (1, 2, 3, ...)
• RATIONAL NUMBERS are numbers that can be expressed as a fraction a/b such that both a and b are integers and b is non-zero. Integers and natural numbers are rational numbers since we can express them with denominator = 1.
• REAL NUMBERS are numbers include natural numbers, integers and rational numbers. It also includes numbers that cannot be expressed as a fraction, e.g. pi, square root of 2

Note: Whole numbers and Complex numbers are not mentioned above.

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[Extension] Going Beyond Real... Imaginary Numbers

Today, we discussed the Real Number System, which the relationship of the families of numbers can be represented in a Venn Diagram.

What's beyond the REAL Number system?

The Imaginary Numbers! [which is not in the "O" level syllabus]
Some of you may be interested to find out more about this...
This will shade some light to the 'mysteries' when we start to discuss "Roots" of numbers