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Need to ask this question again

  • Thread starter Jamin2112
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  • #1
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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????????
 
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Answers and Replies

  • #2
Dick
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According to those definitions, I'll agree. Yes, if it's not defined it's neither continuous nor discontinuous.
 
  • #3
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According to those definitions, I'll agree. Yes, if it's not defined it's neither continuous nor discontinuous.
Weird
 
  • #4
Dick
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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.
 

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