"Lots of tables" is the finite case, for which the AC is a theorem. An infinite set of tables is qualitatively different. An arbitrary f(table) function will ha

"Lots of tables" is the finite case, for which the AC is a theorem. An infinite set of tables is qualitatively different. An arbitrary f(table) function will have to contain an infinite amount of information, which is beyond anything my intuition can grasp. For f(table) functions that contain finite information, the intuition is easy and the AC is reduced to a theorem.