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# Is intersection of two countably infinite sets can be finite?

979899 ###### 2011-10-23 11:20:21

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}.

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## Related Questions There are finite sets, countably infinite sets and uncountably infinite sets. One classification is: finite, countably infinite and uncountably infinite.  One possible classification is finite, countably infinite and uncountably infinite. No. It can be infinite, finite or null. The set of odd integers is infinite, the set of even integers is infinite. Their intersection is void, or the null set. There are many ways of classifying sets. One way is by the size of the set: its cardinality.On this basis a set may beFinite,Countably infinite, orUncountably infinite. 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. A set is finite if there exists some integer k such that the number of elements in k is less than k. A set is infinite if there is no such integer: that is, given any integer k, the number of elements in the set exceed k.Infinite sets can be divided into countably infinite and uncountably infinite. A countably infinite set is one whose elements can be mapped, one-to-one, to the set of integers whereas an uncountably infinite set is one in which you cannot. Closed sets and open sets, or finite and infinite sets. They are both infinite sets: they have countably infinite members and so have the same cardinality - Aleph-null. A finite set is a set that has numbers you can count. Its not like infinite with no end it has an end.  Curiously, both sets are countably infinite and so their cardinality is the same. A finite set is one containing a finite number of distinct elements. The elements can be put into a 1-to-1 relationship with a proper subset of counting numbers. An infinite set is one which contains an infinite number of elements.  Sets are collection of distinct objects. In mathematics there are different types of sets like Finite set, Infinite set, Universal set, subset, equal set, equivalent set. Example of Finite set {1,2,3,4}. Infinite set:{1,2,3....}. The set of your friends is finite. The set of counting numbers (part of which you will use to count your friends) is infinite. The positive integers less than 100 are a finite set. The positive integers greater than 100 are an infinite set. The cardinality of finite sets are the number of elements included in them however, union of infinite sets can be different as it includes the matching of two different sets one by one and finding a solution by matching the same amount of elements in those sets. Finite sets:The counting numbers up to 10{1, 2, 3}The integer factors of 48The members of my immediate familyThe people on EarthThe grains of sand on planet EarthCountable infinite sets:The set of integersThe set of prime numbersThe set of square numbersThe set of rational numbersUncountable infinite sets:The set of real numbersThe set of complex numbers The cardinality of a finite set is the number of distinct elements in the set. For infinite sets, the cardinality is Aleph-Null if the elements of the set can be put into 1-to-1 relationship with the natural numbers: that is, if the set is countably infinite. However, the set of irrational numbers, for example, has a number of elements which is a greater order of infinity (uncountably infinite). It's cardinality is denoted by C, for "continuum". Some finite numbers in a set: the number of digits on your hand, the number of seats on a bus, and the number of people on earth. Some infinite numbers in a set: the number of positive integers and the number of digits in pi. They are sets with a finite number of elements. For example the days of the week, or the 12 months of the year. Modular arithmetic is based on finite sets. 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.) A finite set is a set with a finite number of elements. An infinite set has an infinite number of elements. Intuitively, if you count the elements in a finite set, you will eventually finish counting; with an infinite set, you'll never finish counting. One characteristic of infinite sets is that they can be placed in one-to-one correspondence with proper subsets of the set. For example, if A = {1, 2, 3, 4, ...} (the counting numbers), and B = {2, 3, 4, 5, ...} (the counting numbers, starting at 2), then B is a proper subset of A, and they can be placed in one-to-one correspondence like this: 1 &lt;---&gt; 2; 2 &lt;---&gt; 3; 3 &lt;---&gt; 4, etc. This means that, in a certain sense, the set and its proper subset have "the same number of elements". Such a one-to-one correspondence (between a set and one of its proper subsets) is not possible with finite sets.

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