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Graphs are also really simple structures mathematically. After all, an (undirected) graph is nothing more than a ground set and a collection of its two-element
by eru 2y ago
Graphs are also really simple structures mathematically.
After all, an (undirected) graph is nothing more than a ground set and a collection of its two-element subsets.
It's the same reason why groups crop up so often: groups are also really simple structures, so it's really easy to satisfy their axioms 'by accident'. Same for numbers in general.
- whatshisface 2y agoI don't think that's a full explanation for groups, because groups other than the free or permutation groups are rather "unlikely," in the sense that they're much smaller.
- eru 2y agoOh, I mean they crop up in lots and lots of applications, because their structure is so simple to satisfy. Not that they would crop up, if you somehow randomly generated mathematical structure. The real world, and especially the part of the real world that people engage with, seems to have a lot of simple structures.