e.g.

"here is my lemma that you can divide a polyhedron's surfaces into a network of triangles and remove the triangles one at a time without changing the value of the sum of edges, faces, and vertices"

"well, what if the polyhedron was two pyramids connected at their narrow points?"

"oh, that's not actually a polyhedron, a polyhedron is [refines the definition to exclude this weird case]"

the interesting thing is, this isn't really how math is supposed to work! you're supposed to work from the definitions themselves

secret cabal leader@RussellsBarbershopQuartet@monads.online@dankwraith yeah that's a great point actually; that's fundamentally a rhetorical, not a logical move, and while appearing to be more precise it is actually, just, not.