What is the concept of infinity in set theory?

What is the concept of infinity in set theory?

In set theory, infinity refers to a quantity that is larger than any finite number. It can be used to describe the size of sets that are unbounded.

Can you explain the difference between countable and uncountable infinity?

Sure! Countable infinity refers to sets that can be put into a one-to-one correspondence with the natural numbers, like the set of integers. Uncountable infinity, on the other hand, refers to larger sets, such as the set of real numbers, which cannot be matched with natural numbers.

What are some examples of countably infinite sets?

Examples of countably infinite sets include the set of natural numbers, the set of integers, and the set of rational numbers.

Why is the set of real numbers uncountable?

The set of real numbers is uncountable because, as shown by Cantor's diagonal argument, you cannot list all real numbers in a sequence that includes every possible real number.