👉 Within mathematics, also known as internal mathematics or axiomatic mathematics, is the study of mathematical structures and theories from a foundational perspective, focusing on the logical relationships and axioms that define these systems. It involves defining sets, operations, and relations using a minimal set of axioms to derive all other mathematical truths. This approach aims to provide a rigorous and consistent basis for mathematics, ensuring that all theorems and proofs are logically sound and universally applicable. By starting from basic principles, within mathematics seeks to uncover the underlying structure of mathematical concepts, making it a powerful tool for understanding and developing new theories.
