Is the set of all real numbers is countable?

No, the set of all real numbers is not countable; it is uncountable. This was famously demonstrated by Cantor's diagonal argument, which shows that no listing of all real numbers can include every real number. In contrast, the set of natural numbers is countable, meaning it can be put into a one-to-one correspondence with the integers. Thus, while the natural numbers are countable, the real numbers have a greater cardinality.