Test 

1. The real number system ℝ is best described as:
A. A finite set
B. A non-empty set with operations and ordering
C. Only a set of rational numbers
D. A set without structure

2. Which number system allows solving equations like x + m = n for all integers?
A. ℕ
B. ℤ
C. ℚ
D. ℝ

3. The associative property of multiplication states:
A. ab = ba
B. (ab)c = a(bc)
C. a + b = b + a
D. a(b + c) = ab + ac

4. Which property ensures existence of 0 in ℝ?
A. Inverse
B. Identity
C. Closure
D. Order

5. If a < b and b < c, then a < c. This is:
A. Reflexive
B. Symmetric
C. Transitive
D. Commutative

6. Which number is an irrational number?
A. 1/2
B. 3
C. √2
D. −5

7. The least upper bound is also called:
A. Infimum
B. Supremum
C. Maximum
D. Minimum

8. Which property distinguishes ℝ from ℚ?
A. Commutativity
B. Associativity
C. Completeness
D. Closure

9. If a ≠ 0, then existence of 1/a is guaranteed by:
A. Closure
B. Inverse axiom
C. Order axiom
D. Completeness

10. The set ℚ is incomplete because:
A. It has no integers
B. It lacks ordering
C. It has gaps (missing irrationals)
D. It has no addition

Answer Key (Test)

1-B, 2-B, 3-B, 4-B, 5-C, 6-C, 7-B, 8-C, 9-B, 10-C