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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

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mathsIntegersIntroduction to Integers (directed whole numbers)

Ordinal Property of Integers

This page explains the ordered sequence of integers with negative and positive numbers in number-line.

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One of the fundamental properties of whole numbers is that, numbers are in an ordered sequence representing the magnitude of quantity represented by them.

The whole numbers are in the ordered sequence

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,  etc. This is the ordinal property of whole numbers.

The word "ordinal" means: relating to order or series.

Ordinal property of whole numbers refers to the order 0, 1, 2, 3, et cetera.

Integers are directed whole numbers, having positive and negative numbers.

Do integers have the ordinal property?

Are negative numbers ordered?

Where are the negative numbers placed in reference to the positive numbers?

To answer these questions, let us look at the properties in the number line.

Consider combining the two numbers text(received:)1 and text(received:)2.

The addition is shown in number-line in the figure. The sum is 3.

Consider combining the two numbers text(received:)4 and text(given:)2. The sum is 2.

4+(-2) = 2

Consider combining the two numbers text(received:)1 and text(given:)2.

The addition is shown in number-line in the figure.

1+(-2)=-1.

In the number line the position of -1 is the position before the value 0.

Consider combining the two text(received:)1 and text(given:)2. This is 1+(-2)=-1 and the position of the -1 is fixed to the left of 0. The position of -1 is shown in the figure.

The whole number-line starts from 0 and extends in positive direction.
The integer number-line extends in both the directions as shown.

Consider combining the two numbers text(received:)2 and text(given:)4.

The answer is -2

2+(-4)=-2.

-2 is placed one position before -1.

Extending the placement of -1 and -2, the other negative numbers are placed as shown in the figure.

Summarizing the ordinal property of integers, The ordinal sequence is

cdots,-2, -1, 0, 1, 2, cdots

Ordered Sequence in Integers:
cdots,-2, -1, 0, 1, 2, cdots The integer number line is shown in the figure.

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