What if zero is not a single number, but a set or a category?

Hello!

Sorry for my bad English in advance... I'm just a math lover and amateur. I've been quietly exploring this idea for about 5 years, trying to find mentors or collaborators who could guide and understand this "budding sprout" of mine, but I couldn't find anyone -so I'm sharing here with hope that someone might see value in it. Please view this gently, as a math-loving amateur's small idea.

I'd really appreciate kind guidance and protection for this sprout.Core idea: Let's treat 0 not as a single number, but as a collection/family of distinct quantities. Pick some element θ from that collection to define "zero."For example, define individual exact points on the real line (like 0, 0.4, π etc.) as "basic points."

Assume [0,1] has M such basic points (M quasi-infinite: larger than any real, M + 1 ≠ M), each with "size" θ (infinitesimal-like), and M · θ = 1.This creates a way to handle infinity more precisely (different scales → different "infinities").Payoffs:

Handles special 0/0 cases algebraically (e.g., some physics formulas like Einstein's relative speed when numerator/denominator both go to 0 — compute first, observe second with non-commuting π₀ L'Hôpital's rule is not going to answer it fully philosphically point of view).

Intuitive probability: chance of exact point in [0,1] is θ, in [0,2] is θ/2 → natural ratio 1/2 (classical 0=0 can't express this).

Fractal dimension comes naturally (box-counting with ε = θ gives M^D).

(We're handling pure 0, not standard infinitesimals.)Does this remind anyone of existing work (nonstandard analysis, surreals, Hahn series...)? Is pursuing this (especially for 0/0 in physics or fractals) worth it?

I think it will be contribute to solve some unsovled math problems and am i right or mad?

If anyone wants the full document or to discuss, feel free to DM - I'd be thrilled to share and learn from you!Thank you so much for reading. Your kindness would mean the world to this math-loving amateur.