Appendix on Set Notation
Consider a set S. The notation x S means x is an element of
S; we might also say x belongs to S or x is in S. The notation
x S signies x is some element but x does not belong to S. By
/
T S we mean each element of T also belongs t
Exam 2: Math 3333 Fall 2015
Professor William Ott
Exercise 1. (25; 5 each) Determine if each of the following statements is true or false.
(a) Let a < b be real numbers. If f : [a, b] R is continuous, then f is uniformly continuous on
[a, b].
(b) If the p
MA3333- take home exam, 04/16/13 due 04/23/13
Prof. Daniel Onofrei
University of Houston, Mathematics
April 16, 2013
1. Let f : R R be a monotone function and x0 R. Show that either f is continuous in
x0 or the left- hand and the right-hand limits of f in
Math 3333 FALL 2011
Name:
Test #2
This is a closed-book, no-notes test. Please, write clearly and justify your
arguments using the material covered in class to get credit for your work.
(1)[4 Pts]
(a) State the denition of convergence for a sequence of re
Math 3333 FALL 2011
Name:
Test #3
This is a closed-book, no-notes test. Please, write clearly and justify your
arguments using the material covered in class to get credit for your work.
(1)[4 Pts]
(a) State the denition of continuity for a function f : (a
Exam 1: Math 3333 Fall 2015
Professor William Ott
Exercise 1. (25; 5 each) Determine if each of the following statements is true or false.
(a)
(b)
(c)
(d)
(e)
If the sequence (xn ) is bounded, then (xn ) has a converging subsequence.
For every bounded set