👉 Omega math, also known as Omega calculus or Omega arithmetic, is a formal system designed to extend the basic principles of arithmetic beyond natural numbers. It introduces a new type of variable, the omega symbol (ω), which represents the successor of all natural numbers. This system allows for the formalization of induction principles, enabling proofs by mathematical induction on any well-ordered set, not just natural numbers. Omega arithmetic includes operations for addition, multiplication, and exponentiation, similar to Peano arithmetic, but with the added capability to reason about infinite sequences and structures. This makes it a powerful tool in mathematical logic, particularly in the study of computability and the foundations of mathematics.
