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Ok, you're presenting to an audience consisting of lots of tables, each with at least one person at it. You say: "Will every table please have a representativ
by xamuel 9y ago
Ok, you're presenting to an audience consisting of lots of tables, each with at least one person at it. You say: "Will every table please have a representative stand up."
To question the AC is to suggest that for some configuration of (sufficiently many) tables, it's impossible for the audience to fulfill your request, on account of there not existing a function f(table)=representative. This sounds absurd, because obviously each table can independently choose a representative, and it isn't like they need to coordinate with the other tables in order to fulfill your request.
- cuspycode 9y ago"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.