Readings for Session 11 – (Continued)
More on Properties
A property in mathematics must be true for the entire
universe under discussion. A proposed property can be shown to
not be true by giving
a counterexample.
We only need
one
counterexample to prove that a proposed property is not true.
Example: Is division of whole numbers commutative?
We compare 10 ÷ 2 and 2 ÷ 10. Since 10 ÷ 2 = 5 and 2 ÷ 10 = 0.2
(decimal fractions will be covered later in the course) and 5 ≠
0.2, the two expressions are not equal, 10 ÷ 2 ≠ 2 ÷
10.Therefore, we have made a counterexample to show that
division is not
commutative.
Can you find a counterexample that shows that division is
not associative?
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