Algebra 1: Lesson 1 (Part 2)

Lesson 1
part 2

• Classifying Real Numbers

​Here are 2 subsets of numbers:
A = {2, 4, 6, 8, 10, 12}
B = {3, 6, 9, 12}

​A set of numbers has closure, or is closed, under a given operation (example: adding subtracting) if the outcome of the operation is also a number of the set.

​The set of whole numbers is closed under addition.
2 + 3 = 5
whole number + whole number = whole number

​Sometimes a statement is false, and we need to provide a counterexample! An example that proves a statement is indeed false.

​The set of whole numbers is closed under subtraction.
FALSE
Counterexample:
4 - 6 = -2
whole number - whole number = integer