What is the range of cardinals?

Answer 1

The range of cardinals typically refers to the different sizes of infinite sets in set theory. Cardinal numbers measure the "size" of sets, with each cardinal representing a specific size, such as countable (like the set of natural numbers) or uncountable (like the set of real numbers). The smallest infinite cardinal is denoted as ℵ₀ (aleph-null), representing the size of any countably infinite set, while larger cardinals, such as ℵ₁, ℵ₂, and so on, represent larger infinite sizes. The continuum hypothesis addresses the question of whether there is a cardinal size between ℵ₀ and the cardinality of the continuum (the set of real numbers).