Integers : Predecessor and Successor (Integers)

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Predecessor and Successor (Integers)

what you'll learn...

overview

It was earlier studied that the integers are in an ordered sequence. In this page, the following are explained.

• the number preceding in the order is the predecessor of a given number.

• the number following in the order is the successor of a given number.

The predecessor and successor are explained with the number-line too.

one less or more

The predecessor of $3$ $3$ is $2$ $2$ . Predecessors were introduced in whole numbers. Predecessor of a number is computed by subtracting $1$ $1$ from that number.

The successor of $3$ $3$ is $4$ $4$ . Successors were also introduced in whole numbers. Successor of a number is computed by adding $1$ $1$ to that number.

By first principle, the whole numbers are in an ordered sequence. $0, 1, 2, cdots$

Predecessor of a number is placed prior to that number and so, is is $1$ less than the number.

Successor of a number is placed after that number and so, it is $1$ more than the number.

additionally given or received

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 less is equivalent of one additionally given.

One more of $text(received:)3$ is $text(received:)4$ . One more is equivalent of one additionally received.

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

and one additionally given makes it $-4$ .

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

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

and one 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 $cdots,-2, -1, 0, 1, 2, cdots$ .
The predecessor and successor of a number is placed prior to or after to the number.

examples

What is the predecessor of $-5$ ?
The answer is ' $-6$ '. In the ordered sequence $cdots,-7,-6,-5,-4,-3,-2,-1, 0, 1, 2, cdots$ , $-6$ is prior to $-5$ . So, $-6$ is the predecessor of $-5$ .

What is the successor of $-7$ ?
The answer is ' $-6$ '. In the ordered sequence $cdots,-7,-6,-5,-4,-3,-2,-1, 0, 1, 2, cdots$ , $-6$ succeeds $-7$ . So, $-6$ is the successor of $-7$ .

summary

Integers (the directed whole numbers) are in an ordered sequence, given as $cdots,-2, -1, 0, 1, 2, cdots$ .
The predecessor a number is placed prior to that number. The predecessor can be computed by subtracting $1$ from the number.

The successor of of a number is placed after to that number. The successor can be computed by adding $1$ to he number.

Outline

The outline of material to learn integers is as follows.

Note: click here for detailed outline of Integers (directed numbers)

→ Introduction to Directed Numbers

→ Handling Direction

→ Ordinal Property

→ Sign and Absolute Value

→ Comparing Integers

→ Predecessor & Successor

→ Largest & Smallest

→ Ascending & Descending

→ Addition: First Principles

→ Addition: Simplified Procedure

→ Subtraction: First Principles

→ Subtraction: Simplified Procedure

→ Multiplication: First Principles

→ Multiplication: Simplified Procedure

→ Division: First Principles

→ Division: Simplfied Procedure

→ Numerical Expressions with Integers

→ PEMA / BOMA