It sounds like your naive view was better than mine if you already had that idea, as that’s basically Nate’s point. I see the general ‘definition’ of symmetry in math or physics as “if I change X in Y way, it doesn’t ‘really’ change”. In physics symmetries usually mean there’s a conservation law. Specifically that’s only true for continuous ones, but you can still get important stuff out of the discrete ones like the CPT theorem or fermions vs bosons for exchange symmetry
It sounds like your naive view was better than mine if you already had that idea, as that’s basically Nate’s point. I see the general ‘definition’ of symmetry in math or physics as “if I change X in Y way, it doesn’t ‘really’ change”. In physics symmetries usually mean there’s a conservation law. Specifically that’s only true for continuous ones, but you can still get important stuff out of the discrete ones like the CPT theorem or fermions vs bosons for exchange symmetry