#TOC #Examples

Question

Give examples of:

Countable Infinite Set

Countable Finite Set

Uncountable Finite Set

Uncountable Infinite Set

Answer 1

How can finite set be uncountable? It's finite.

About rest -

1.) Set of natural numbers $N$ .

2.) Any finite set is countable.

4.) $2^{N} $ Power set of countably infinite set is uncountable.

Comments

@Reshu $ingh There are a lot of trivial doubts coming from your side. I would suggest you to first try to find the solutions in standard books and then post anything in the community. 
Thanks. 

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hmmm :)

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ok :)

Answer 2

• countable infinite set : rational number, integer or recursive language .
• countable finite set : it is simple any set which have finite number of element 

ex : set of string of 2 length {aa,ab,ba,bb}

• uncountable infinite set : real number , set of all language or not recursive ennum language .

​​​​​​​uncountable finite set , it is not possible