# Finding interior point and accumulation point

• Mar 10th 2013, 01:22 PM
jhh1014
Finding interior point and accumulation point
For the set S = {1,2,3,4} U (5,6), what is
• an interior point of S?
• A point S n delS?
• A point in delS - S
• An accumulation point of S that is not in S (and a sequence that converges to it)
• A ball about the point x = 5.03 that is contained in S?
• Mar 10th 2013, 01:29 PM
Plato
Re: Finding interior point and accumulation point
Quote:

Originally Posted by jhh1014
For the set S = {1,2,3,4} U (5,6), what is
• an interior point of S?
• A point S n delS?
• A point in delS - S
• An accumulation point of S that is not in S (and a sequence that converges to it)
• A ball about the point x = 5.03 that is contained in S?

What is the definitions of these terms?
I have never seen delS. What does it mean?

I will do one for you. The interior is $\displaystyle S^o=(5,6)~.$

You must post some efforts.
• Mar 10th 2013, 01:51 PM
jhh1014
Re: Finding interior point and accumulation point
∂S, is the boundary of S. I think the ∂S is the set {1,2,3,4,5,6}, but I am not sure. Would that make a point in S ∩ ∂S be any of those numbers?
• Mar 10th 2013, 02:22 PM
Plato
Re: Finding interior point and accumulation point
Quote:

Originally Posted by jhh1014
∂S, is the boundary of S. I think the ∂S is the set {1,2,3,4,5,6}, but I am not sure. Would that make a point in S ∩ ∂S be any of those numbers?

That is completely standard notation. But it is not 'del" it is delta.
In LaTeX it is [TEX]\delta(S)[/TEX] gives $\displaystyle \delta(S)$.

Please learn to use LaTeX. On the advanced toolbar the $\displaystyle \boxed{\Sigma}$ gives the [TEX]..[/TEX] wraps .