Chapter 1, Problem 453RE

In the following exercises, determine which of the following are (a) counting numbers (b) whole numbers.

2, 99

To determine

(a)

The counting numbers in the given set.

Answer to Problem 453RE

  $2$ and $99$

Explanation of Solution

Given information:

The set of numbers is $0,2,99$ .

Algebra represents word and idea with the help of symbols and numbers. In algebra, the numbers used to count the objects are the most basic numbers; they are $1,2,3,4,\mathrm{5...}$ and so on.

All these numbers are known as counting numbers. Here, " $\mathrm{.....}$ " this notation is ellipsis which is a way to show "and so on" which means the same pattern continues endlessly. All the counting numbers are natural numbers.

Thus, counting numbers starts from 1 and continues endlessly following the same pattern as shown below:

  $1,2,3,4,\mathrm{5...}$ and so on.

Calculation:

The given numbers are $0,2$ and $99$ .

The counting numbers starts from $1$ and continues endlessly following the same pattern. For example, $1,2,3,4,5,\dots \mathrm{..}$ and so on.

In counting numbers, zero is not included therefore, $2$ and $99$ are counting numbers.

To determine

The whole numbers in the given set.

Answer to Problem 453RE

  $0,2$ and $99$

Explanation of Solution

Given information:

The set of numbers is $0,2,99$ .

In the history of mathematics, the discovery of number zero is a biggest achievement.

A new set of numbers is form if zero is included in the set of counting numbers. This new set of numbers is known as whole numbers.

Counting numbers and whole numbers can be seen on a number line as shown below:

  

In the above number line, the point at number zero is known as origin. There are equally spaced points on the right of the origin labelled with the counting numbers. When pairing of a point and number takes place, the number is called the coordinate of the point.

Therefore, whole numbers are counting numbers and zero. The pattern is as follows:

  $0,1,2,3,4,5,\mathrm{.......}$ and so on.

Calculation:

The given numbers are $0,2$ and $99$ .

The whole numbers are counting numbers and zero. The pattern is as follows:

  $0,1,2,3,4,5,\mathrm{.......}$ and so on.

Since, whole numbers includes $0$ in the counting numbers therefore, $0,2$ and $99$ are whole numbers.