Developing a theoretical foundation for the laws of conservation

Finite divisibility of general systems is shown. Based on this result, Lavoisier’s Axiom, introduced in 1789, is verified by using the concept of basic particles, where a basic particle is one particle which can no longer be divided into smaller ones. The conservation principle of ancient atomists is recasted and proved mathematically, based on which the law of conservation of matter‐energy can be seen clearly. A brief history of atoms, elements, and laws of conservation is given and some important open questions are posed.