Large Cardinials

Large Cardinals are certain extraordinarily powerful concepts in set theory, the branch of mathematics dealing with collections of objects. They are hypothetical infinite sizes (called "cardinals") that go beyond the commonly known infinities, like countable infinity (the size of natural numbers). Large Cardinals possess strong properties that imply they are "much bigger" or "more comprehensive" than smaller infinities, and their existence has deep implications for the structure of sets and the foundations of mathematics. While their existence cannot be proven with current mathematics, they are important in understanding the landscape of infinite sizes and the limits of mathematical theories.