Properties (axioms) of addition

Question 1

Closure

Answer 1

all answers fall into the original set.

ex: if you add two even numbers, the answer is still an even number, therefore the set of even numbers is closed (has closure) under addition

if you add to odd numbers, the answer is not an odd number, therefore the set of odd numbers is not closed under addition

Question 2

Commutative

Answer 2

means that the order does not make a difference

EX: 2 + 3 = 3 + 2 or a+b = b+a

note: does not hold for subtraction

Question 3

associative

Answer 3

means that the grouping does not make any difference

ex: (2+3) + 4 = 2+(3+4)

does not work for subtraction

Question 4

additive inverse

Answer 4

opposite of the number

any number plus its additive inverse equals 0