Assuming the axiom of choice there exist subsets of reals that are not measurable. But without AC we can construct models in which every subset of reals is measurable. So why do we stick to ZFC, is knowing that every surjection in Set splits or that a ball can be cut into 5 pieces and reassembled into two balls identical as the one we started with more important that being able to measure every subset of reals?
Assuming the axiom of choice there exist subsets of reals that are not measurable...
Carson Thomas
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Ryan Martin
Axiom of choice was a mistake.
James Davis
Choicefags BTFO
Tyler Taylor
>Assuming the axiom of choice there exist subsets of reals that are not measurable. But without AC we can construct models in which every subset of reals is measurable. So why do we stick to ZFC, is knowing that every surjection in Set splits or that a ball can be cut into 5 pieces and reassembled into two balls identical as the one we started with more important that being able to measure every subset of reals?
What are your preferred axioms?
Eli Fisher
ZF+countable choice
Camden Martinez
You obviously don't understand what an axiom is, so why do you imagine you have anything interesting to contribute to this discussion?
Blake Harris
I do, I'm just wondering why AC is preferred over other axioms
Thomas Lee
It's preferred by people who prefer it, and not by people who don't. There's no law that says you have to use an axiom, you use the axioms that are useful for the type of math you want to do.
Joshua Ross
Its impossible to order some sets. How would select an element from them?
Lincoln Foster
>How would select an element from them?
Just choose any element from the set, the set doesn't have to be orderable for you to be able to take a countable subset of it.