If something is undefined does that mean it doesn't exist?

Question

Here is the question: If f is undefined at x=c, then the limit of f(x) as x approaches 2? True of False?

Answer 1

First, We can't tell if it's true or false unless we know what the function is. Second, this is a math question, not a physics question

Answer 2

If f is undefined at x = c, then it means it is impossible to compute the value of the function f, at the point when x = c.  So to get an idea as to what the value at x = c should be, you can use methods such as finding the limit of the function as x approaches c.

Answer 3

Mumba-

You are discussing (and asking about) continuity.

If f(x) does not exist but the limit of f(x) exists at some x value, then the function is discontinuous at that x.  The discontinuity is called removable, i.e., you can "fix it" by redefining f(x) = lim f(x) at that x value.

Undefined does not mean that something does not exist.

Plane, set, point, line...are all undefined in mathematics, but we believe that they exist.  

Now 1/0 log(0) and SQRT(-a) where a>0 are undefined in the Real domain, and they do not exist...

So whether something undefined exists is dependent upon context.