> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/100-fundamentals/terms/arithmetic.md).

# Arithmetic

Arithmetic deals the 4 basic operations: add, sub, mul, div.

Add and sub on the one hand, and mul and div on the other are each other's opposite operations. However, sub and div are somewhat of the second-class operations not only because they are easily defined in terms of add/mul with appropriate invertability axioms:

* sub: 9 - 5 = 9 + (-5)
* div: 5 ÷ 3 = 5 *⅓ = 5* 3⁻¹

After all, add/mul could be defined in terms of sub/div as well, but the bigger reasons for their "lesser" treatment is because sub and div do not obey all the axioms that they inverses do; namely, unlike add and mul, sub and div do not uphold the axioms of associativity, commutativity and closure (totallity).