Q: Is the intersection of two infinite sets always an infinite set?

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No, they do not.

union means to group the given sets. where as intersection means to pick out the common elements from the given sets. if set a has 1,2,3 elements and B has 1,2,3,4,5. then its union will have 1,2,3,4,5 as its elements. and its intersection will have 1,2,3 as its elements.

If the set has "n" elements, then you can make 2n different subsets. The number of subsets will always be greater than the size of the set, both for finite and for infinite sets.

1]empty set 2]singleton set 3]finite set 4]infinite set >.<

ExplanationFormally, two sets A and B are disjoint if their intersection is the empty set, i.e. if This definition extends to any collection of sets. A collection of sets is pairwise disjoint or mutually disjoint if, given any two sets in the collection, those two sets are disjoint.Formally, let I be an index set, and for each i in I, let Ai be a set. Then the family of sets {Ai : i ∈ I} is pairwise disjoint if for any i and j in I with i ≠ j,For example, the collection of sets { {1}, {2}, {3}, ... } is pairwise disjoint. If {Ai} is a pairwise disjoint collection (containing at least two sets), then clearly its intersection is empty:However, the converse is not true: the intersection of the collection {{1, 2}, {2, 3}, {3, 1}} is empty, but the collection is not pairwise disjoint. In fact, there are no two disjoint sets in this collection.A partition of a set X is any collection of non-empty subsets {Ai : i ∈ I} of X such that {Ai} are pairwise disjoint andSets that are not the same.

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No, they do not.

No. Say for example interval A is (-inf, 0), and interval B is (0, inf). Even though they are both infinite, their intersection is the empty set (i.e. they have nothing in common). The same applies to sets. That being said, it is entirely possible for two infinite intervals' intersection to be infinite. All that is required is that one is a subset of the other (one set contains all of the other set, for example A = (0, inf) and B = (1, inf). Here, A contains all of B, and therefore, their intersection is B. This means that their intersection is infinite.)

Easily. Indeed, it might be empty. Consider the set of positive odd numbers, and the set of positive even numbers. Both are countably infinite, but their intersection is the empty set. For a non-empty intersection, consider the set of positive odd numbers, and 2, and the set of positive even numbers. Both are still countably infinite, but their intersection is {2}.

No, only if both sets are empty. The intersection of disjoint sets is always empty.

Not necessarily. The odd integers and the even integers are two infinitely large sets. But their intersection is the null (empty) set.

You normally do not have an intersection of only one set. The intersection of a set with itself is the set itself - a statement that adds little value. The intersection of two sets is the set which contains elements that are in each of the two sets.

There are finite sets, countably infinite sets and uncountably infinite sets.

is the result after doing intersection on 2 or more sets. It contains the elements which are common to all the sets on which intersection were done.

The concept of closure: If A and B are sets the intersection of sets is a set. Then if the intersection of two sets is a set and that set could be empty but still a set. The same for union, a set A union set Null is a set by closure,and is the set A.

Given two or more sets there is a set which is their union and a set which is there intersection. But, there is no such thing as a "union intersection set", as required for the answer to the question.

The way I understand it, a finite set can not be an infinite set, because if it were an infinite set, then it would not be a finite set, and the original premise would be violated.

That is called the intersection of the sets.