axioms

Axioms are fundamental principles or starting points in a system of thought, such as mathematics or logic, that are accepted without proof. They serve as the basic building blocks from which other statements or theorems are derived. Think of axioms as self-evident truths or rules that everyone agrees upon to develop consistent and logical structures. For example, in mathematics, the statement "Through any two points, there is exactly one straight line" is an axiom. They are essential for establishing a common foundation in formal systems, allowing us to explore and prove more complex ideas.