Sect 1.6 Properties of Differences
Definition
of subtraction: For all real numbers a and b a b = a + (- b)
Subtraction is not a separate operation but rather is a convenient way of writing the addition of the additive inverse of a number.
Ex. 13
(- 4)
To subtract
4
from
13,
we add the opposite of
4
to
13;
14
+ 4 = -9
You know that the real numbers are closed under addition (if you add two real numbers, you get a real number), and since every real number has an additive inverse, then the real numbers are also closed under subtraction.
Ex. Is subtraction commutative?
8 5 = 3 5
8 = -3 Not
commutative
Ex. Is subtraction associative?
6 (2
9) = 6
(- 7) (6
2)
9 = 4 - 9
= 13 = -5 Not associative