Intersection of an infinite set

michonamona · 2010-05-29T20:25:39+00:00

Let G_{n} = (-1/n,1/n) for all n in N let G= \bigcap^{\inft}_{n=1}

Thread starter michonamona
Start date May 29, 2010
Tags

Infinite Intersection Set

In summary, the intersection of an infinite set is the set of all elements that are common to two or more infinite sets. It is denoted by the symbol ∩ and can be an infinite set itself. This differs from the intersection of finite sets, which will always be a finite set. The intersection of infinite sets can also be an empty set, depending on the sets being intersected. This operation is one of the basic set operations and can be extended to any number of infinite sets. It can also be used to solve real-world problems in various fields such as genetics and computer science.

May 29, 2010

michonamona

Let [tex]G_{n}[/tex] = (-1/n,1/n) for all n in N

let [tex] G= \bigcap^{\inft}_{n=1} [/tex]

Physics news on Phys.org

May 29, 2010

irycio

So, what's the question/problem?? The intersection is simply 0 (zero, a single number). Hence the intersection of an infinite number of open sets is not necessarily open, whereas the union is always open, as is the finite intersectiion of them. With the closed sets, it's the other way round :).

1. What is the definition of an intersection of an infinite set?

The intersection of an infinite set is the set of all elements that are common to two or more infinite sets. It is denoted by the symbol ∩ and is represented as A ∩ B, where A and B are two infinite sets.

2. How is the intersection of infinite sets different from the intersection of finite sets?

The main difference between the intersection of infinite sets and finite sets is that an infinite set can have an infinite number of elements, while a finite set has a limited number of elements. This means that the intersection of infinite sets can also be an infinite set, whereas the intersection of finite sets will always be a finite set.

3. Can the intersection of infinite sets be an empty set?

Yes, the intersection of infinite sets can be an empty set, depending on the sets being intersected. If there are no common elements between the infinite sets, then the intersection will be an empty set. For example, the intersection of the set of all even numbers and the set of all odd numbers is an empty set.

4. How is the intersection of infinite sets related to set operations?

The intersection of infinite sets is one of the basic set operations, along with union, complement, and difference. It is used to find the common elements between two or more sets. The intersection operation can also be extended to any number of infinite sets, not just two.

5. Can the intersection of infinite sets be used to solve real-world problems?

Yes, the intersection of infinite sets can be used to solve real-world problems. For example, in genetics, the intersection of infinite sets can be used to find the common characteristics between different species. In computer science, it can be used to find common features between different software programs. Overall, the intersection of infinite sets is a useful tool in many fields of science and mathematics.