Skip to Main Content
Real Analysis
book

Real Analysis

by V. Karunakaran
May 2024
Intermediate to advanced content levelIntermediate to advanced
585 pages
15h 38m
English
Pearson India
Content preview from Real Analysis
“real: chapter_05” 2011/5/22 22:55 page 18 #18
5-18 Real Analysis
2. Take f (x) as the characteristic function of the closed inter-
val [0, 1]. One can easily verify that f (0+) = 1, f (0) =
0, f (1+) = 0, f (1) = 1 so that 0 and 1 are points of dis-
continuities of the first kind. On the other hand, every point in
(0, 1) or (1, ) or (−∞,0) is a point of continuity for f .
3. f (x) =
1
x
for x > 0
0 for x 0
Here f :
R R has discontinuities of the second kind at x = 0
since f (0) = 0, f (0+) does not exist.
4. f (x) =[x], the greatest integer less than or equal to x. This
function f :
R R is continuous at all points other than integers
and
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Make: Calculus

Make: Calculus

Joan Horvath, Rich Cameron
Complex Analysis

Complex Analysis

ITL Education

Publisher Resources

ISBN: 9781299447561Publisher Website