Sizes of infinity fall into two broad classes: countable infinities, and uncountable infinities.
A set \(S\) is uncountable if it is not countable.
- Uncountability: Intro (Math 1)
Not all infinities are created equal. The infinity of real numbers is infinitely larger than the infinity of counting numbers.
- Uncountability: Intuitive Intro
Are all sizes of infinity the same? What does “the same” even mean here?
- Uncountability (Math 3)
Formal definition of uncountability, and foundational considerations.
- Real numbers are uncountable
The real numbers are uncountable.
Mathematics is the study of numbers and other ideal objects that can be described by axioms.