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 |
|||
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 |