Question

Are the following sets countable, infinitely countable, or not countable? 1- The set of all odd integers? 2- The set of all prime numbers < 1000? 3- The set of all real numbers between 0 and 2?

Answer 1

1. Infinitely countable

2.Countable

3.Not countable

Explanation:

Infinitely countable set : The set whose cardinality is equal to cardinality of set of natural numbers.Then the set is called infinitely countable

Countable set : The set whose cardinality is finite or equals to any constant value then, the set is called countable.

Not countable : The set whose cardinality is not equal to any constant value or not equal to cardinality of set of natural number .Then the set is called not countable.

1.The set of odd integers is countable infinite because its cardinality is equal to cardinality of natural number set

2.The set of all prime numbers less than 1000 .It means the cardinality of set of all prime numbers less than 1000 is equal to any finite number or any constant value.Therefore, the set of all prime number less than 1000 is a countable set .

3.The set of all real numbers between 0 and 2 is not countable because infinite real numbers lies between 0 and 2 .Hence, the set is not countable