Need to ask this question again

[Jamin2112]

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?

 

[Dick]

According to those definitions, I'll agree. Yes, if it's not defined it's neither continuous nor discontinuous.

 

[Jamin2112]

According to those definitions, I'll agree. Yes, if it's not defined it's neither continuous nor discontinuous.

Weird

 

[Dick]

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.