Undefined value and Infinite value

[salil87]

Hi
When we say that a function has an undefined value at a particular time does it mean it is infinite at that time? I mean most of the time it is infinite. But is an infinite value always called undefined and is an undefined value always infinite? If so why is it called undefined? Why not infinity?
Thanks
Salil

 

[I like Serena]

Welcome to PF, salil87!

Infinite and undefined are different things.
For a function, infinite usually implies undefined.
But undefined does not have to be infinite.

For instance, the function log(x) is negative infinity at zero and as such undefined at zero.
But for negative values of x, log(x) is simply undefined (but not infinite).

 

[Deveno]

for a slighty silly example, consider the empty function, which has no domain.

its graph is, of course, blank, but infinity doesn't even enter the picture.

 

[HallsofIvy]

Or: define f(x)= 3x for x> 0, f(x)= 2x for x< 0. Then f(0) is, literally, "undefined".

 

[salil87]

Thanks a lot. :-)

Thanks
Salil