Comment Comment by azeemba As the author points out that Banach-Tarski theorem is an example of hard-to-accept result that comes out of the easy-to-accept axiom of choice.There is a popular quote that related to this:> The axiom of choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?From https://en.wikipedia.org/wiki/Axiom_of_choiceAxiom of choice, the well-ordering principle and Zorn's lemma are equivalent statements (any one proves the other two). But each has a very different "believability" feel to it. parent azeemba 3 years ago
There is a popular quote that related to this:
> The axiom of choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?
From https://en.wikipedia.org/wiki/Axiom_of_choice
Axiom of choice, the well-ordering principle and Zorn's lemma are equivalent statements (any one proves the other two). But each has a very different "believability" feel to it.