>I was proving that it doesn't matter if the construction is visual, symbolic or just verbose sentences. Those are just the props. To be mathematics, whatever you are doing has to be justified by a reasonable mathematical argument.
Maybe what bugs you is that the picture doesn't have a "sequence". The relationships are just all displayed and interrelate all at once. But that's closer to the actual content of mathematical abstractions.
Logic or argument is just one way of taking a tour around those concepts, and the trip can vary somewhat in its sequence from one tour guide to another. You should know that Godel proved you can't get a tour guide to take you everwhere. Math != logical deduction.