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Thought-Process to Discover Knowledge

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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.

negative numbers in 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`.

negative numbers in number line Consider combining the two numbers `text(received:)4` and `text(given:)2`. The sum is `2`.

`4+(-2) = 2`

negative numbers in number line 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`. negative numbers in number line 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.

negative numbers in number line 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.

negative numbers in number line 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`negative numbers in number line The integer number line is shown in the figure.

                            
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