This document contains two rounds of questions about concepts in real analysis. Round I defines and explains properties of real numbers including the associative and commutative laws of addition and multiplication, identity elements, existence of inverses and negatives, and distributivity. Round II explains additional concepts such as the absolute value property, monotone properties of addition and multiplication, triangle inequality, transitivity, algebraic and transcendental numbers, enumerability, law of trichotomy, and infimum. The document was prepared by an assistant professor as a study guide or practice questions for students.

1. QUIZ

2. REAL ANALYSIS
Unit I
Prepared BY
Ms. R. Umadevi
Assistant Professor,
Bon Secours College For
Women, Thanjavur

3. ROUND I
Find me

4. a + ( b+ c ) = ( a + b) + c

5. Associative law of addition

6. a + 0 = 0 + a = a

7. Identity element for addition

8. a + b = b + a = 0

9. Existence of negatives

10. a + b = b + a

11. Commutative law of addition

12. a ( b c ) = ( a b ) c

13. Associative law of multiplication

14. a.1 = 1.a = a

15. Identity element for multiplication

16. a b = b a = 1

17. Existence of inverse

18. a b = b a

19. Commutative law of multiplication

20. a ( b + c ) = a b + a c

21. Distributivity of Multiplication over addition

22. ( a + b ) c = a c + b c

23. Distributivity of Multiplication over addition

24. ROUND II
Explain

25. Absolute Value

26. 






0
0
x
if
x
x
if
x
x

27. Monotone Property for
addition

28. a > b => a + c > b + c

29. Triangle Inequality

30. y
x
y
x 



31. Transitivity

32. c
a
then
c
b
b
a 

 ,
,

33. Algebraic

34. A real number is said to be
algebraic if it is the root of
some polynomial equation
with rational coefficients

35. Monotone property for
multiplication

36. a > b and c > 0 => ac > bc

37. Transcendental

38. A real number is said to be
transcendental if it is not
algebraic

39. Enumerable

40. A set is said to be enumerable,
if there exists a one to one
mapping from the set N of all
natural numbers onto the set S

41. Law of trichotomy

42. a > b, a = b, b > a

43. Infimum

44. If the set of all lower bounds of
a set S of real numbers has a
greatest member, say t, then t
is said to be a greatest lower
bound or an infimum of S