III B.Sc., Mathematics

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