MHB Is 7 an irrational number in the set of integers?

[nycfunction]

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]

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]

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]

You make your post unnecessarily confusing by using "Z" for the set of all integers and to mean an individual integer.

 

[topsquark]

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

 

[HOI]

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.