# Relationship between integers and whole numbers

### Math Forum: Ask Dr. Math FAQ: Integers, Rational Numbers, Irrational Numbers

In fact, the only difference between the set of natural numbers and the set of whole numbers is that the set of whole numbers {0, 1, 2, 3, 4, 5, } includes zero ( 0). an integer? What's the difference between a rational number and an irrational number? Integers are the whole numbers, negative whole numbers, and zero. A summary of Classification of Numbers in 's Integers and Rationals. Learn exactly what Natural Numbers, Whole Numbers, Integers, and Rationals. Natural.

This is perhaps understandable when you consider areas such as set theory, where zero may be used to represent the cardinality of an empty set cardinality in this case refers to the number of items a set contains, and is therefore very much related to counting. One thing that almost everyone agrees on is that the set of natural numbers does not include negative numbers.

When talking about whole numbers, things are not so clear cut, since there is no formal definition of what constitutes a whole number.

Some people think that the set of whole numbers should be considered to include negative numbers, as well as zero. If that were the case, however, there would be no distinction between whole numbers and integers. Fortunately, when it comes to integers, there is no controversy about the definition. This does however leave us with the question of zero - does this belong to the positive integers or the negative integers?

Positive integers must, by definition, be greater than zero. Similarly, negative integers must be less than zero, so zero can't belong to either set of numbers. We can get around the limitations of the term positive integer which doesn't include zero by using the term non-negative integer which by definition does include zero.

Actually, we rarely bother to use a plus sign to indicate positive numbers, since the absence of a minus sign is usually taken to mean that the number is positive. If we do have to write a number that has a negative value, we usually place a minus sign to the left of the number e. When computers have to deal with integers, life is not quite so simple. A computer can store the absolute value of any integer from zero to two-hundred and fifty-five in a single byte eight bits.

If we want the computer to know whether the number is positive or negative, we can use one of the bits usually the left-most or most significant bit to indicate the sign. A zero indicates that the number is positive, while a one indicates that the number is negative.

## Whole Numbers and Integers

The magnitude of the largest positive or negative number we can represent as a signed integer using a single byte is therefore only half that of the largest unsigned integer, since we have one less bit available with which to represent it. Programmers or students studying computer science will probably be aware that there are several quite different and sophisticated ways in which computers can represent signed numbers internally.

Most of us, however, do not have to worry about such things, interesting as they may be. What is of interest for the purposes of this discussion is that we can get around any possible ambiguity surrounding the definition of natural numbers using one of the groups of integers defined above. If we consider the set of natural numbers to be all of the positive whole numbers excluding zero which is the traditional definitionwe can substitute the term positive integers for the term natural numbers.

If, on the other hand, we want to include zero in our definition of the natural numbers, we can instead use the term non-negative integers. Special symbols are used to represent both the set of natural numbers and the set of integers. In order to indicate whether or not zero is considered to be included in the set of natural numbers, some form of additional notation is often used.

### Whole numbers & integers (article) | Khan Academy

Additional notation can be used to signify a subset of integers. The mathematical properties of natural numbers and integers differ slightly. The sum or product of any two natural numbers will itself be a natural number. Any help you can give would be greatly appreciated.

**Natural Numbers, Whole Numbers, and Integers , Intermediate Algebra , Lesson 1**

Thanks, Rina Hallock Date: Making a tree diagram of the various number systems is a nice way to show their relations - in particular, noting which sets of numbers are subsets of other numbers. For example, the natural numbers also called "counting numbers are a subset of the whole numbers.

## Whole numbers & integers

There is no subset of largest numbers. The list that your daughter's teacher gave her includes several redundancies. For example, you asked about "surds". A surd is another name for an irrational number.

- Natural Numbers and Integers
- Integers and rational numbers

Thus, sqrt 2 is a surd. It is also an irrational number. This means that when you try to evaluate it as a decimal, it neither repeats nor terminates. A decimal number that repeats is 0. A number that terminates is 0. In the first case, 0. Both of these numbers are rational numbers because they can be expressed as the ratio between two integers. Your daughter was correct in separating the real numbers into two mutually exclusive sets: These two sets of numbers have no numbers in common: Each set is also infinite: Rational Numbers A Venn diagram is a good way to "see" the relations among different sets of numbers: