## def'n of Limit Point? and limit.

I know that there are different definitions for a limit point .

"A number such that for all , there exists a member of the set different from such that .

The topological definition of limit point of is that is a point such that every open set around it contains at least one point of different from ."-MATHWORLD

Are they all equivalent, when defining "the limit of f"? Or, this may help too, does my definition of a limit sound correct?...(bold-faced variables are vectors)

Let f: U->R^n
Let a be an element of the reals such that for all delta' >0 there exists an x in U, different than a, such that ||x-a||<delta'.
We say that lim f(x)=L as x->a, if for every epsilon>0 there exists a delta''>0 so that if ||x-a||<delta'' then ||f(x)-L||<epsilon.

Also, Is it right that I used delta' and delta"?
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 Is it necessary that I write U to be an open set?
 Limit point in this sense is not the same thing at all as the limit of a function as it aproaches a point. They are two different things.

## def'n of Limit Point? and limit.

i know that, but you DO need to define a limit point in order to define the limit. It would really help if you could please look at my definition of a limit.
 To be honest, I'm not sure I understand the question.

 Quote by calvino Let f: U->R^n Let a be an element of the reals such that for all delta' >0 there exists an x in U, different than a, such that ||x-a||a, if for every epsilon>0 there exists a delta''>0 so that if ||x-a||
In set form, the definition then reads that for every open set U about a in R, there exists an open set V in Rn about L that contains f(U), the image of U under f.
If D is the domain of f, then we see that L is a limit point of f(D).
 Recognitions: Gold Member Science Advisor Staff Emeritus Except for one small point, since x and a are real numbers you mean |x-a|, not ||x-a||, Your definition of limit is correct. You really have 2 definitions: "Let a be an element of the reals such that for all delta' >0 there exists an x in U, different than a, such that ||x-a||a, if for every epsilon>0 there exists a delta''>0 so that if ||x-a||