Question on continuity

Homework Statement

Ok my book tells me

A function f is continuous at a number a if

lim x->a f(x) = f(a)

Like sure it makes sense but i'm wondering if someone can tell me the exceptions to this definition or if it's just completely wrong

you know like sort of like how when I was told many years ago

only to find out it did...

like so can someone tell me if the definition my book gives me is strictly speaking correct... please tell me all exceptions or if it's wrong like for example maybe the complex logarithm maybe?

Thanks

Mark44
Mentor

Homework Statement

Ok my book tells me

A function f is continuous at a number a if

lim x->a f(x) = f(a)

Like sure it makes sense but i'm wondering if someone can tell me the exceptions to this definition or if it's just completely wrong
There are no exceptions.
you know like sort of like how when I was told many years ago

Why are you dragging this up again? It was explained to you that equations have domains on which they are defined. If x is a real number, then cos(x) = -2 has no solutions. If x is a complex number, then this equation has solutions.
only to find out it did...

like so can someone tell me if the definition my book gives me is strictly speaking correct... please tell me all exceptions or if it's wrong like for example maybe the complex logarithm maybe?

Thanks

Thanks... I just wanted to make sure =). Yes I know they have domains but when their not specified one cannot assume that x is in the set of reals, especially when you were taught it about other number systems...

I just wanted to make sure and thanks!

Mark44
Mentor
The context of the problem usually makes it clear what the domain for an equation is.

Dick
Homework Helper

Homework Statement

Ok my book tells me

A function f is continuous at a number a if

lim x->a f(x) = f(a)

Like sure it makes sense but i'm wondering if someone can tell me the exceptions to this definition or if it's just completely wrong

you know like sort of like how when I was told many years ago

only to find out it did...

like so can someone tell me if the definition my book gives me is strictly speaking correct... please tell me all exceptions or if it's wrong like for example maybe the complex logarithm maybe?

Thanks

The Attempt at a Solution

What you quoted is the DEFINITION of continuity. Not buying a definition is a little strange. Do you have a different definition of continuity?