Q: What is the accumulation point of irrational points?

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No, not all adherent points are accumulation points. But all accumulation points are adherent points.

Yes, every point in an open set is an accumulation point.

There are no boundary points.

No. It could be a rational or an irrational

There should be no points after the decimal point.

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No, not all adherent points are accumulation points. But all accumulation points are adherent points.

Yes, every point in an open set is an accumulation point.

If you have a finite set of points (call them A1, A2, A3...), then you have a finite set of distances to the points. So for any point B, simply pick a distance D that's smaller than the distance between B and A1, the distance between B and A2, and so on. (This is possible, since there a finite number of points.) ================================================ Since there are no points within distance D of B (because this is how you chose D), point B can not be an accumulation point (because an accumulation point must have points within any given distance of it)

An accumulation point, or limit point, for a set S is a point x (not necessarily in S) such that any open set containing x also contains a point (distinct from x) that's in S. More intuitively, it means that by choosing points in S, we can get as close as we want to x without actually reaching it. For example, consider the set S={1,1/2,1/3,1/4,...} (in the real numbers). 0 is an accumulation point for S, because any open set containing 0 would have to contain all between 0 and some ε>0, which would include a point (actually, an infinite amount of points) in S. But 1/5, for example, is not an accumulation point for S, because we can take the open interval (11/60,9/40) which doesn't contain any points in S other than 1/5. Not all sets have an accumulation point. For example, any set of a finite amount of real numbers can't have an accumulation point. Another example of a set without an accumulation point is the integers (as a subset of the real numbers). However, over the real numbers, any bounded infinite set has an accumulation point. In a general topological space, any infinite subset of a compact set has an accumulation point.

Complex analysis is a metric space so neighborhoods can be described as open balls. Proof follows a. Assume that the set has an accumulation point call it P. b. An accumulation point is defined as a point in which every neighborhood (open ball) around P contains a point in the set other than P. c. Since P is an accumulation point, I can choose an open ball around P that has a diameter less than the minimum distance between P and all elements of the finite set. Therefore there exists a neighbor hood around P which contains only P. Therefore P is not an accumulation point.

In mathematics, an accumulation point is a point such that every neighbourhood of the point contains at least one point in a given set other than the given point.

There are no boundary points.

Training certificates.

No. It could be a rational or an irrational

There is no number which can be rational and irrational so there is no point in asking "how".

The condition is known as myofascial pain syndrome (MPS).

It is rational.A number cannot be both rational and irrational.