Determine all the accumulation point.

  • Thread starter furi0n
  • Start date
  • Tags
    Point
In summary, an accumulation point, also known as a limit point, is a point in a set where every neighborhood contains infinitely many points of the set. To determine all the accumulation points in a set, you can list all the points, find the limit points of each point, eliminate any duplicate limit points, and the remaining limit points will be the accumulation points. An accumulation point and a cluster point are similar, but an accumulation point can be a point in the set itself while a cluster point must be a limit point. A set can have more than one accumulation point, and determining these points can aid in understanding the behavior and characteristics of the set and can be useful in various areas of mathematics.
  • #1
furi0n
19
0
I've faced with some problem in Math. Analysis books of Tom Apostol,
For example, (-1)n+ 1/m, n,m=1,2,3,4,5...

i think there is no accumulation point but how should i prove this?

thanks for your helps...
 
Physics news on Phys.org
  • #2
Since the 1/m term -> 0, -1 and 1 are accumulation points.
 

FAQ: Determine all the accumulation point.

What is an accumulation point?

An accumulation point, also known as a limit point, is a point in a set where every neighborhood of the point contains infinitely many points of the set.

How do you determine all the accumulation points in a set?

To determine all the accumulation points in a set, you can follow these steps:

  1. List all the points in the set.
  2. Find the limit points of each point in the set.
  3. Eliminate any duplicate limit points.
  4. The remaining limit points will be the accumulation points of the set.

What is the difference between an accumulation point and a cluster point?

An accumulation point and a cluster point are both points in a set where every neighborhood contains infinitely many points of the set. The main difference is that an accumulation point can be a point in the set itself, while a cluster point must be a limit point of the set.

Can a set have more than one accumulation point?

Yes, a set can have more than one accumulation point. In fact, a set can have infinitely many accumulation points.

What is the importance of determining accumulation points in a set?

Determining accumulation points can help in understanding the behavior and characteristics of a set. It can also be useful in solving problems in various areas of mathematics such as calculus, topology, and analysis.

Similar threads

I Determination of error in interpolating polynomial
Replies
5
Views
1K
I Proof of 1/(x^2) Not Having Limit at 0
Replies
5
Views
2K
Problem 1-23 and 1-24 from Spivak's Calculus on Manifolds
Replies
6
Views
1K
I What is the difference between these two power series theorems?
Replies
5
Views
917
I Uncertainties accumulate when measuring longer lengths?
Replies
7
Views
858
I Discrete Subrings of Complex Numbers: Topology of Rings
Replies
11
Views
2K
MHB Complex Derivative .... Remark in Apostol, Section 16.1 .... ....
Replies
2
Views
1K
I Physics domain analysis of Voltage drop in series resistor
Replies
7
Views
2K
I Proving Alternating Derivatives with Induction in Mathematical Analysis I
Replies
10
Views
3K
I Question about uniform convergence in a proof
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top