The Set of Mathematics
Suppose I am making a set, its empty at first, I take a random research paper and add it to set, paper’s references and citations too in set, reference’s references and citations too. I continue this process for all the papers, books, etc. How big could it be?
To well define the set, we take these assumptions:
1. The set must be in maths only. Can be of both pure math or applied.
2. The interdisciplinary will be in the boundary of the set.
3. For subjects like Physics, Biology, etc. we can have similar sets and a superset of them can have all the subjects. That way a clear structure of all sets would be there.
4. I’m thinking like a Venn diagram, if the universal set is all subjects, then interdisciplinary in boundaries so some will be in the intersection and some entirely in maths.
5. Papers with 0 citations and 0 references are not counted
6. Only standard books and reference papers are eligible. Like if someone published a paper in Arabic in 1800, it's not eligible. Or a local book, it also not counted.
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So, a Babylonian tablet or ancient things, they are not eligible and we can ignore. I’m making the set based on these conditions/assumptions.
It may be beneficial to use Bibliometric analysis to study it. However, it is peculiar in terms of countability.
What do you think in this manner it would become an uncountable set or infinite countable set? We are adding finitely many papers at each step but still I can’t draw a conclusion regarding its countability…
Even if the references in all are more than N but there are branches then the references with their sub references can be treated in form of finite product which again will be countable.
And I think that this brings us down back to our very initial question of existence or building of such a set, that it would be a never-ending process.
