which properties of real numbers do not hold true for natural numbers?

you know the properties like commutative properties of addition and all that. Which ones are not natural numbers. Ill list em:

Properties of the Real Numbers

For all real numbers a, b, and c:

1. Commutative Property for Addition: a + b = b + a

2. Commutative Property for Multiplication: ab = ba

The commutative properties state that two numbers may be added or multiplied in any order.

3. Associative Property for Addition: a + (b + c) = (a + b) + c

4. Association Property for Multiplication: a(bc) = (ab)c

For the associative properties, the order of the terms or factors remains the same; only the grouping is changed.

5. Identity Property for Addition: There is a unique real number, 0, such that a + 0 = a and 0 + a = a

The identity property for addition tells us that adding 0 to any number will not change the number.

6. Identity Property for Multiplication: There is a unique real number, 1, such that a·1 = a and 1·a = a

The identity property for multiplication tells us that multiplying any number by 1 will not change the number.

7. Inverse Property for Addition: Each nonzero real number a has a unique additive inverse, represented by –a, such that

a + (-a) = 0 and –a + a = 0

Additive inverses are called opposites.

8. Inverse Property for Multiplication: Each nonzero real number a has unique multiplicative inverse, represented by , such that and

Multiplicative inverses are called reciprocals.

9. Distributive Property: a(b + c) = ab + ac