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 |
|||
Complete the following table:
Numbers |
Commutative for |
|||
Addition |
Subtraction |
Multiplication |
Division |
|
Rational numbers |
Yes |
... |
||
Integers |
No |
|||
Whole numbers |
Yes |
|||
Natural numbers |
No |
Complete the following table:
Numbers |
Associative for |
|||
Addition |
Subtraction |
Multiplication |
Division |
|
Rational numbers |
No |
|||
Integers |
Yes |
|||
Whole numbers |
Yes |
|||
Natural numbers |
No |
If a property holds for rational numbers, will it also hold for integers? For whole Numbers? Which will? Which will not?