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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 <---> 2; 2 <---> 3; 3 <---> 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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Q: What are finite and infinite sets?

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Finite

The positive integers less than 100 are a finite set. The positive integers greater than 100 are an infinite set.

finite

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.

A finite set has a finite number of elements, an infinite set has infinitely many.

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

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.

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Closed sets and open sets, or finite and infinite sets.

Closed sets and open sets, or finite and infinite sets.

Closed sets and open sets, or finite and infinite sets.

One classification is: finite, countably infinite and uncountably infinite.

finite and infinite sets

A finite set is a set that has numbers you can count. Its not like infinite with no end it has an end.

Finite, countably infinite and uncountably infinite.

One possible classification is finite, countably infinite and uncountably infinite.

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.

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