Caption: Hello everyone! This project is a model exploring the mathematical foundation of arithmetic operations, aiming to demonstrate that all familiar operations can be built from a single fundamental operation. Specifically, the entire system in this project does not use multiplication, exponentiation, or other pre-existing advanced operations, but relies solely on the successor operation (incrementing by 1) combined with a repeating structure. Starting with addition defined as repeating +1, multiplication is built as repeating addition, exponentiation as repeating multiplication, and continues to expand to tetration, pentation, and hexation, following the hyper-operator system in mathematics. Each “level” in the project corresponds to a new growth stage, where the operation at the higher level depends entirely on and only on repeating the operation of the level immediately below, not on any shortcuts. Example: • Level 1 describes addition as a repetition of +1 • Level 2 builds multiplication from addition • Level 3 represents exponentiation as a repetition of multiplication • Higher levels illustrate how super-advanced operations arise from the same principle This project demonstrates the extremely rapid growth of advanced operations, while clearly reflecting how complex mathematical structures can arise from very simple rules. Click “see inside” to observe in detail how each operation is built from the ground up and how the entire system operates with just +1. =================================== Level 0: Succession Level 1: Addition Level 2: Multiplication Level 3: Exponentiation Level 4: Tetration Level 5: Pentation Level 6: Hexation
