# Let Z = Set of Integers

#### nycfunction

##### Banned
Determine if the number 7 is a natural number, an integer, a rational or irrational number.

I know that integers include positive and negative numbers and 0.

Let Z = the set of integers

Z = {. . . -2, -1, 0, 1, 2, . . .}

I also know that any integer Z can be written as Z/1 = Z.

I will conclude by saying the following:

7 = 7/1

So, 7 is a natural number, an integer and a rational number (because it can be written as a fraction over 1).

Does this apply to all integers, Z?

#### Olinguito

##### Well-known member
Hi nycfunction .

So, 7 is a natural number, an integer and a rational number (because it can be written as a fraction over 1).
That’s correct.

Does this apply to all integers, Z?
Let’s take an example, $-1$. It is an integer, but is it a natural number?

#### nycfunction

##### Banned
Hi nycfunction .

That’s correct.

Let’s take an example, $-1$. It is an integer, but is it a natural number?
The integer -1 is not a natural number aka whole number. This means not all integers Z are natural or whole numbers. Negative numbers are excluded.

#### HallsofIvy

##### Well-known member
MHB Math Helper
You make your post unnecessarily confusing by using "Z" for the set of all integers and to mean an individual integer.

#### topsquark

##### Well-known member
MHB Math Helper
The integer -1 is not a natural number aka whole number. This means not all integers Z are natural or whole numbers. Negative numbers are excluded.
Many would agree but there is confusion about whether we should count 0 as a whole number. Some say yes, some say no. You can definitely say that all positive integers are whole numbers.

-Dan

#### Country Boy

##### Well-known member
MHB Math Helper
Also, you do not address the last part of the problem. Is "7" an irrational number? What is the definition of "irrational number"? In fact, all of these are just a question of whether you know the definitions.