0 like 0 dislike
0 like 0 dislike
what's the craziest consequence of Zorn's lemma u know?

4 Answers

0 like 0 dislike
0 like 0 dislike
Not sure what you mean by "craziest" (most counterintuitive?), but I'll tell you a very important one that links algebra to geometry: in an arbitrary nonzero commutative ring, the intersection of all prime ideals is the set of nilpotent elements. So if an element of a nonzero commutative ring vanishes modulo all prime ideals, then that element might not be 0 but at least some power of it is 0.
0 like 0 dislike
0 like 0 dislike
The algebraic closure of the field of p-adic numbers Q_p is isomorphic to C.

This is so bizarre that many well-known mathematicians prefer to avoid it. For example, morphisms from the algebraic closure of Q_p to C appear in an essential way in Deligne’s second paper on the Weil conjectures and there he remarks that we prefers not to believe in such an isomorphism.
0 like 0 dislike
0 like 0 dislike
The Well-ordering Theorem.
0 like 0 dislike
0 like 0 dislike
The axiom of choice. Such a ridiculous property  
:)

Related questions

0 like 0 dislike
0 like 0 dislike
12 answers
joixlee asked Jun 21
Importance of the role of First Order Logic (FOL) in understanding higher level mathematics
joixlee asked Jun 21
by joixlee
0 like 0 dislike
0 like 0 dislike
3 answers
ItalyatUNESCO asked Jun 21
What's the best way to find the roots of an arbitrary polynomial over the complex numbers?
ItalyatUNESCO asked Jun 21
0 like 0 dislike
0 like 0 dislike
20 answers
GeorgiaBrougham asked Jun 21
What are the classical mathematics textbooks of the 20th Century?
GeorgiaBrougham asked Jun 21
0 like 0 dislike
0 like 0 dislike
41 answers
serapduygulu asked Jun 21
What is the best layman interpretation of any mathematical concept you have seen?
serapduygulu asked Jun 21
0 like 0 dislike
0 like 0 dislike
2 answers
hiroki_noda asked Jun 21
Is anyone familiar with the book, “Topics in the Theory of Numbers,” by Erdős and Surányi?
hiroki_noda asked Jun 21

24.8k questions

103k answers

0 comments

33.7k users

OhhAskMe is a math solving hub where high school and university students ask and answer loads of math questions, discuss the latest in math, and share their knowledge. It’s 100% free!