Question

Using complete sentences, explain what an infinite set is. In your answer give at least two examples of infinite sets

Answer 1

Set of integers is countably infinite set

Set of Irrational number

Explanation:

A set when it has cardinality less than the cardinality of natural set.Then the set is called finite set.

When the set is not finite then the set is called infinite set.

Infinite set are of two types:

1.Countably infinite

2.Uncountable

1.Countable infinite set: when the cardinality of set is equal to cardinality of natural set .Then the set is called countably infinite .

Example:Set of integers is countably infinite set.

2.Uncountable : When the set is not countable or not finite then the set is called uncountable.The cardinality of uncountable set is greater than the cardinality of natural set.

Example:Set of Irrational number