Need to ask this question again

  • Thread starter Thread starter Jamin2112
  • Start date Start date
Click For Summary

Homework Help Overview

The discussion revolves around the concept of continuity and discontinuity of functions, specifically in the context of definitions provided in a homework assignment. Participants are examining the implications of a function being undefined at certain points.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are exploring the definitions of continuity and discontinuity, questioning what it means for a function to be undefined. There is a focus on whether an undefined function can be classified as continuous or discontinuous.

Discussion Status

Some participants express agreement with the idea that if a function is not defined, it cannot be classified as either continuous or discontinuous. Others reflect on specific examples to illustrate their points, indicating a productive exploration of the topic.

Contextual Notes

There is mention of a specific function, f(x)=sqrt(x), which is only defined for non-negative values, raising questions about its continuity at negative inputs. This highlights the nuances in the definitions being discussed.

Jamin2112
Messages
973
Reaction score
12
A few days ago, I asked about the continuity of a function, in regards to a problem on my homework. Something still seems wrong, even though today my professor insisted that the given definitions are correct. Look here: http://www.math.washington.edu/~sullivan/3261_sp10.pdf"

A function f(x,y) is continuous at a point (x0,y0) if f(x,y) is defined at (x0,y0), ...

A function f(x,y) is discontinuous at a point (x0,y0) if f(x,y) is defined at (x0,y0), ...


So if a function isn't defined, then it is neither continuous or discontinuous?
 
Last edited by a moderator:
Physics news on Phys.org
According to those definitions, I'll agree. Yes, if it's not defined it's neither continuous nor discontinuous.
 
Dick said:
According to those definitions, I'll agree. Yes, if it's not defined it's neither continuous nor discontinuous.

Weird
 
Jamin2112 said:
Weird

Well, think about f(x)=sqrt(x). That's only defined for x>=0. You certainly don't want to say it's continuous at x=(-1). And it also sounds a little weird to say it's discontinuous at x=(-1). It's just not defined. Not all that strange.
 

Similar threads

A few questions to make sure I understand Fourier series
  • · Replies 3 ·
Replies
3
Views
2K
Confirm Limit Existence for Function f w/o Piecewise Def.
  • · Replies 4 ·
Replies
4
Views
2K
Is It Possible to Invert a Homotopy?
  • · Replies 5 ·
Replies
5
Views
1K
A contradiction? - Calculus III Question
  • · Replies 11 ·
Replies
11
Views
3K
Linear Approximation: Finding Point P
  • · Replies 1 ·
Replies
1
Views
4K
Is the given function continuous at x= 0? f(x) = {sin(1/x) if x≠0, 1
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Gradient Vectors: Perpendicular to Level Curves
  • · Replies 4 ·
Replies
4
Views
3K
Understanding the solution to a calculus problem (removable discontinuities)
  • · Replies 2 ·
Replies
2
Views
2K
Real Analysis question - Show that the derivative is continuous.
  • · Replies 1 ·
Replies
1
Views
2K
Complex Analysis Qn: Show Constant Function in B(z0; r)
  • · Replies 13 ·
Replies
13
Views
3K