What Mathematics Is The Most Fundamental ? Felix

Standard mathematics involves such notions as infinitely small/large, continuity and standard division. This mathematics is usually treated as fundamental while finite mathematics is treated as inferior. Standard mathematics has foundational problems (as follows, for example, from Gödel’s incompleteness theorems) but it is usually believed that this is less important than the fact that it describes many experimental data with high accuracy. We argue that the situation is the opposite: standard mathematics is only a degenerate case of finite one in the formal limit when the characteristic of the ring or field used in finite mathematics goes to infinity. Therefore foundational problems in standard mathematics are not fundamental.