Numbers

Closed under

 

Addition

Subtraction

Multiplication

Division

Rational numbers

Yes

Yes

Yes

No

Integers

Yes

Yes

Yes

No

Whole numbers

Yes

No

Yes

No

Natural numbers

Yes

No

Yes

No

" />

Numbers

Closed under

 

Addition

Subtraction

Multiplication

Division

Rational numbers

Yes

Yes

Yes

No

Integers

Yes

Yes

Yes

No

Whole numbers

Yes

No

Yes

No

Natural numbers

Yes

No

Yes

No

" />

Numbers

Closed under

 

Addition

Subtraction

Multiplication

Division

Rational numbers

Yes

Yes

Yes

No

Integers

Yes

Yes

Yes

No

Whole numbers

Yes

No

Yes

No

Natural numbers

Yes

No

Yes

No

" />

Relations and Functions

Relations and Functions

Question

Fill in the blanks in the following table:

Numbers

Closed under

 

Addition

Subtraction

Multiplication

Division

Rational numbers

Yes

Yes

 

No

Integers

 

Yes

 

No

Whole numbers

...

 

Yes

 

Natural numbers

 

No

   
 

Answer

Using the closure property over addition, subtraction, multiplication and division for rational numbers, integers, whole-numbers and natural numbers, we have:

Numbers

Closed under

 

Addition

Subtraction

Multiplication

Division

Rational numbers

Yes

Yes

Yes

No

Integers

Yes

Yes

Yes

No

Whole numbers

Yes

No

Yes

No

Natural numbers

Yes

No

Yes

No

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