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I don’t understand your point. There are seemingly bizarre consequences of choice and of the negation of choice. They revolve around uncountable sets. For me
by syzarian 4y ago
I don’t understand your point. There are seemingly bizarre consequences of choice and of the negation of choice. They revolve around uncountable sets. For me, the bizarre thing is uncountable sets. I’m fine with them existing in ZFC and use them when doing mathematics but uncountability is bizarre.
- bmacho 4y agoI had no real point. Just imagine it, and laugh, because it is a funny scenario. It doesn't need uncountable sets btw, countable infinite many prisoners, and 2 colors do the trick. I don't know what you mean by uncountable sets are bizarre. Newtonian physics uses a lot of uncountable sets, and it is consistent witch our everyday experiences, isn't it? Or things like Banach-Tarski would appear anyway? Do you have some examples?
- syzarian 4y agoMost of the bizarre things that happen in set theory come from uncountability. Of course there are lots of examples where uncountable sets aren’t bizarre. Physics uses real manifolds and other continuous mathematics to model reality but this doesn’t mean reality contains any actual uncountable sets.