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Let Z = Set of Integers

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nycfunction

Banned
May 24, 2019
13
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

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Apr 22, 2018
251
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nycfunction

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May 24, 2019
13
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

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MHB Math Helper
Jan 29, 2012
1,151
You make your post unnecessarily confusing by using "Z" for the set of all integers and to mean an individual integer.
 

topsquark

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MHB Math Helper
Aug 30, 2012
1,120
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

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MHB Math Helper
Jan 30, 2018
371
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.