:- 5) Find an example of a countable family of continuous functions f, [0, 1] → [0 + ∞[, i € N, such that the function infien fi: [0, 1] → [0, +∞[, defined by +∞ inf f(t) = inf f(x), IEN i=0 is finite everywhere, but not continuous.
:- 5) Find an example of a countable family of continuous functions f, [0, 1] → [0 + ∞[, i € N, such that the function infien fi: [0, 1] → [0, +∞[, defined by +∞ inf f(t) = inf f(x), IEN i=0 is finite everywhere, but not continuous.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
3.5
![**Example Problem: Countable Family of Continuous Functions**
Find an example of a countable family of continuous functions \( f_i : [0,1] \rightarrow [0,+\infty[, \, i \in \mathbb{N} \), such that the function
\[
\inf_{i \in \mathbb{N}} f_i : [0,1] \rightarrow [0,+\infty[
\]
defined by
\[
\inf_{i \in \mathbb{N}} f_i(t) = \inf_{i=0}^{+\infty} f_i(x),
\]
is finite everywhere, but not continuous.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa68164dd-6bba-4aa5-92bc-4824a71db092%2Fa6c58846-b9c8-4945-bb40-7ba9e82f10cc%2Fpjdop8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Example Problem: Countable Family of Continuous Functions**
Find an example of a countable family of continuous functions \( f_i : [0,1] \rightarrow [0,+\infty[, \, i \in \mathbb{N} \), such that the function
\[
\inf_{i \in \mathbb{N}} f_i : [0,1] \rightarrow [0,+\infty[
\]
defined by
\[
\inf_{i \in \mathbb{N}} f_i(t) = \inf_{i=0}^{+\infty} f_i(x),
\]
is finite everywhere, but not continuous.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
