3 июн. 2023 г. · Dependent choice is also not enough to prove the existence of non measurable subsets of the reals. Could one not argue that such a system gains ...

7 сент. 2016 г. · The axiom of choice is not only (in my opinion of course) counterintuitive, but it also has a lot of counterintuitive consequences.

16 июн. 2016 г. · If you have confidence in the axiom of choice, you have to conclude that your intuition about situations involving infinity is hopelessly wrong.

16 февр. 2015 г. · No, you don't need the full strength of the axiom of choice. Given the context of functional analysis, I'd add the axiom of dependent choice to ...

22 окт. 2014 г. · Simply: because it leads to more interesting mathematics. For example, a cool fact not about vector spaces: AC is equivalent to AxA having the same cardinality ...

26 июн. 2021 г. · If we can program some theoretical machine to do an infinite amount of picking for us, that's like the Axiom of Choice, and if it's even ...

28 нояб. 2023 г. · Without the axiom of choice, a set can be infinite, but have no countably infinite subset. Indeed, without the axiom of choice, there can be an infinite set.

6 дек. 2016 г. · The axiom of choice is the equivalent to saying: The cartesian product of a group of nonempty sets is itself nonempty. Why is it controversial?

30 мая 2022 г. · Axiom of choice is controversial because it allows you to make an infinite amount of decisions. In real life, one cannot make an infinite amount ...

22 июн. 2020 г. · Here's the AoC definition they use: Let C be a collection of nonempty sets. Then we can choose a member from each set in that collection.