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How many integers are there between $ - 10$ and $2$ and how many whole numbers are there between them? Write them.

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Last updated date: 19th Jul 2024
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Answer
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Hint: Here we have to find the numbers of integers between $ - 10$ and $2$ and also the whole numbers between them. Integers can be defined as the numbers which include positive numbers, negative numbers and also zero but no fractions are included whereas whole numbers can be defined as the numbers without fractions, and they are a collection of positive integer numbers and zero.

Complete step by step answer:
In Mathematics we have different types of numbers and each number is different from one another and they are categorized into different groups of integers and whole numbers are one of them. Integers can be defined as the numbers that can be either zero, positive or negative numbers but integers can never be a fraction, a decimal or a percent. The symbol used to represent integers is Z. Examples of integers are $ - 2, - 1,0,1 \ldots $.

The representation of integers can be done on a number line by representing positive numbers on the right side of zero and negative numbers on the left side of zero.Whole numbers can be defined as the collection of all natural numbers including zero. Whole numbers as the name implies whole so they can never be a fraction or decimal numbers and they can be represented by the symbol W. Examples of whole numbers are \[0,1,2,3 \ldots \].

We have to find the integers and whole numbers between $ - 10$ and $2$. So, the integers between $ - 10$ and $2$ are $\left\{ { - 9, - 8, - 7, - 6, - 5, - 4, - 3, - 2, - 1,0,1} \right\}$. Now, the whole numbers between $ - 10$ and $2$. We will only include the positive numbers and zero between these two numbers as in whole numbers we cannot include negative numbers.So, the whole numbers between $ - 10$ and $2$ are $\left\{ {0,1} \right\}$.

Hence, there are $11$ integers and $2$ whole numbers between $ - 10$ and $2$.

Note: All whole numbers can be an integer but not all integers can be whole numbers as in whole numbers we only include positive numbers and zero but in integers we include all positive and negative numbers and zero. Integers can be defined as the set of positive whole numbers and their opposites, including zero such as the opposite of $2$ is $ - 2$.