Why is 1+1=2?

Abstract

Too often we take the method of decimal addition to be the definition of addition. We clarify this misunderstanding by first giving a definition of addition and then proving that the decimal addition method is both sound and complete with respect to the given definition. By showing the soundness and completeness of decimal addition with respect to the addition of natural numbers, we actually propose a new approach to algorithm correctness. We also discuss the differences between our logic approach and the traditional axiomatic approach.