👉 Arbitrary math refers to mathematical concepts and systems where the underlying structures, operations, or even the symbols used are not naturally derived from the real world but rather chosen for their convenience, elegance, or utility. For example, in number theory, we often work with prime numbers or modular arithmetic without these being the only possible number systems. Similarly, in algebra, we might define operations on abstract algebraic structures like groups or rings where the usual rules of arithmetic don't apply, but these operations still satisfy certain axioms. This abstraction allows mathematicians to explore complex ideas and solve problems in a more generalized and powerful way, even if the specifics don't mirror everyday experiences. The "arbitrariness" lies in the fact that these choices are made for mathematical purposes, not because they reflect natural phenomena.
