Notation for set of limit points?

Thread starter nonequilibrium
Start date Feb 1, 2012
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Limit Notation Points Set

In summary, the notation for a set of limit points is usually written as L(A), lim(A), or lim<sub>x→∞</sub> A, where A is the original set. The set of limit points is defined as the set of all points that can be approached by a sequence of points in the original set. It has several properties, including being closed, containing all its accumulation points, and being equal to the closure of the original set. The set of limit points is closely related to the concept of a limit in calculus, representing the set of all possible values that a function can approach as the input variable approaches a specific value. The notation for a set of limit points is important as it allows for the expression and

Feb 1, 2012

nonequilibrium

Is there a common notation for the set of limit points of a set?

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Feb 1, 2012

micromass

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Apparently [itex]A^\prime[/itex] is often used.

Feb 1, 2012

nonequilibrium

Oh, lucky break, I had encountered that before but couldn't guess what it meant.

Thanks.

What is the notation for a set of limit points?

The notation for a set of limit points is usually written as L(A), where A is the original set. It can also be written as lim(A) or lim_x→∞ A.

How is the set of limit points defined?

The set of limit points is defined as the set of all points that can be approached by a sequence of points in the original set. In other words, a point is a limit point if there exists a sequence of points in the original set that converges to that point.

What are the properties of a set of limit points?

There are several properties of a set of limit points, including that it is always closed, it contains all its accumulation points, and it is equal to the closure of the original set.

How is the set of limit points related to the concept of a limit?

The set of limit points is closely related to the concept of a limit in calculus. It represents the set of all possible values that a function can approach as the input variable approaches a specific value.

Why is the notation for a set of limit points important?

The notation for a set of limit points is important because it allows us to express and analyze the behavior of a function near a specific point. It also helps us better understand the properties and relationships between different sets and their limit points.