Question

Give an example of a countable collection of finite sets whose union is not finite .​

Answer 1

Answer:

Define An = n where n ∈ N. Then ∪nAn = N which is infinite. ... If the set of all irrational numbers were countable, then R would be the union of two countable sets, hence countable.

Step-by-step explanation:

An = n where n ∈ N. Then ∪nAn = N which is infinite

Answer 2

Below is an example of a countable collection of finite sets whose union is not finite.

To find: An example of a countable collection of finite sets whose union is not finite.

Step-by-step explanation:

• A finite set is a set of items that have a fixed number of elements. A finite set is a collection of elements that can be enumerated and completed informally.

• The union in set theory is the set of all items in a collection of sets. It's a basic procedure that allows sets to be merged and joined. A nullary union is a union of zero sets that is, by definition, equivalent to the empty set.

Example:

$A_n=$Divisors of $n$

All A is finite, but $UA_n$∈N$=n-{0}$

$X_n=$ complex roots of $(1 + x + x^{2} + ... + x_n)$

That is the set of all possible complex numbers which are the $n^{th}$ root of 1, for any n∈N.