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Thought-Process to Discover Knowledge

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Predecessor and Successor (Integers)

It was earlier studied that the integers (both positive and negative numbers) are in an ordered sequence. In this page, the predecessor and successor of an integer is explained.



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The predecessor of `3` is `2`. Predecessors were introduced in whole numbers.

The successor of `3` is `2`. Successors were also introduced in whole numbers.

The whole numbers are in an ordered sequence. `0, 1, 2, cdots`

Predecessor of a number is 1 less than the number.

Successor of a number is 1 more than the number.

Integers are directed whole numbers.

`3` is `text(aligned:)3` or `text(received:)3`

`-3` is `text(opposed:)3` or `text(given:)3`

One less of `text(received:)3` is `text(received:)2`.

One more of `text(received:)3` is `text(received:)4`.

`-3` represents `text(given:)3`

and `1` additionally given makes it `-4`.

So, the predecessor of `-3` is `-4`.

`-3` represents `text(given:)3`

and `1` additionally received makes it `-2`.

So, the successor of `-3` is `-2`.

Integers (the directed whole numbers) are also in an ordered sequence.

The ordered sequence of integers is given as `cdots,-2, -1, 0, 1, 2, cdots`.

Solved Exercise Problem:

What is the predecessor of `-5`?

  • `-6`
  • `-6`
  • `-4`
  • Predecessor does not exist for negative numbers

The answer is '`-6`'. In the ordered sequence `cdots,-7,-6,-5,-4,-3,-2,-1, 0, 1, 2, cdots`, `-6` is prior to `-5`.

Solved Exercise Problem:

What is the successor of `-7`?

  • `-6`
  • `-6`
  • `-8`
  • successor does not exist for negative numbers

The answer is '`-6`'. In the ordered sequence `cdots,-7,-6,-5,-4,-3,-2,-1, 0, 1, 2, cdots`, `-6` succeeds `-7`.

                            
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