A set is denumerable if its elements can be counted, either finite or infinite, and each element can be assigned a unique positive integer as its index.
To show that a set is denumerable, you need to provide a one-to-one correspondence between the elements of the set and the positive integers. This means that each element in the set can be assigned a unique positive integer as its index.
A denumerable set is a type of countable set where each element can be assigned a unique positive integer as its index. A countable set, on the other hand, is a more general term that includes both denumerable sets and sets that can be put into a one-to-one correspondence with the positive integers.
Yes, an infinite set can be denumerable. As long as each element in the set can be assigned a unique positive integer as its index, the set can be considered denumerable, regardless of its size.
No, the set of real numbers is not denumerable. It is uncountable, meaning that it cannot be put into a one-to-one correspondence with the positive integers. This is because there are infinitely many real numbers between any two given real numbers, making it impossible to assign a unique positive integer to each element.