MA 403 Real Analysis I
Exercise Set 1
(1) Using only the Algebraic Properties I-1 to I-5 prove the following.
(i) 0 is the unique real number such that a + 0 = a for all a R. In other words, if
some z R is such that a + z = a for all a R, then z = 0.
(ii)

Indian Institute of Technology Bombay
MA 403: Real Analysis
Mid Semester Examination
Date & Time: 7.9.2008, 2.30 PM 4.30 PM
Max Marks : 30
Note: Begin the answer to each question on a new page of the answerbook. Answers
to all the subparts of a question s

MA 403 Real Analysis I
Exercise Set 3
(1) A set D is said to be countable if it is finite or if there is a bijective map from
N to D. A set that is not countable is said to be uncountable.
(i) Show that the set cfw_0, 1, 2, . . . of all nonnegative integ

Indian Institute of Technology Bombay
MA 403: Real Analysis
Quiz II
Date & Time: 07.10.2008, 6.00 PM 7.00 PM
Max Marks : 10
Note: The five questions below carry 2 marks each. You are not required to solve
the Bonus Problems. But you are welcome to attempt

Indian Institute of Technology Bombay
MA 403: Real Analysis I
Quiz I
Date & Time: 18.8.2008, 6.00 PM 7.00 PM
Max Marks : 10
Note: Each of the five questions below carries 2 marks. You are not required to
solve the Bonus Problems. But you are welcome to at