maths > integers

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.

Integers are directed whole numbers.

$3$ is $\textrm{\left(a l i g \ne d\right\rangle} 3$ or $\textrm{\left(r e c e i v e d\right\rangle} 3$

$- 3$ is $\textrm{\left(o p p o s e d\right\rangle} 3$ or $\textrm{\left(g i v e n\right\rangle} 3$

One less of $\textrm{\left(r e c e i v e d\right\rangle} 3$ is $\textrm{\left(r e c e i v e d\right\rangle} 2$. One less is equivalent of one additionally given.

One more of $\textrm{\left(r e c e i v e d\right\rangle} 3$ is $\textrm{\left(r e c e i v e d\right\rangle} 4$. One more is equivalent of one additionally received.

$- 3$ represents $\textrm{\left(g i v e n\right\rangle} 3$

and one additionally given makes it $- 4$.

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

$- 3$ represents $\textrm{\left(g i v e n\right\rangle} 3$

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