I know that there are different definitions for a limit point .(adsbygoogle = window.adsbygoogle || []).push({});

"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

Letabe an element of the reals such that for alldelta'>0 there exists anxin U, different thana, such that ||x-a||<delta'.

We say that lim f(x)=Lasx->a, if for everyepsilon>0 there exists adelta''>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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# Def'n of Limit Point? and limit.

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