Zev Chonoles
Reputation
99/100 score
 2d comment Angle between two vectors? @Pedro77: However, my answer is correct formula for any two vectors in any $\mathbb{C}^n$. Note that the cross product of two vectors doesn't even make sense unless they are in $\mathbb{R}^3$ (Wikipedia). 2d comment Angle between two vectors? @Pedro77: No, it's not wrong. For two vectors $\mathbf{a},\mathbf{b}\in\mathbb{R}^3$, it's true that $$\tan^{-1}\left(\frac{\|\mathbf{a} \times \mathbf{b}\|}{\mathbf{a} \cdot\mathbf{b}}\right) =\tan^{-1}\left( \frac{\|\mathbf{a}\|\|\mathbf{b}\| \sin(\theta)}{\|\mathbf{a}\| \|\mathbf{b} \|\cos(\theta)}\right)= \tan^{-1} \left(\frac{\sin(\theta)}{\cos(\theta)}\right)= \tan^{-1}(\tan(\theta))=\theta$$ As was explained in the answer you linked to, that approach is chosen for numerical stability, which is a computational concern. Two formulas can both be correct but have different stability. 2d answered If $f'(x)\rightarrow \infty$ then $f(x)\rightarrow\infty$? 2d comment Conjecture: Partitioning $\Bbb N$ into parts that sum to $13^i$ Why not write the far clearer sentence "there exists a partition $\mathbb{N}=\bigcup A_i$ for which the sum of the elements of $A_i$ is $13^i$"? Apr 27 revised Primary decomposition in a Dedekind Domain added 5 characters in body Apr 27 comment Why is the set of all half-lines in the real numbers not a topological space? @BrahadeeshS.: The axiom you're thinking of is that any union of open sets is open. Apr 27 answered Why is the set of all half-lines in the real numbers not a topological space? Apr 25 awarded Enlightened Apr 23 revised On the degree of cyclotomic fields extension. added 446 characters in body Apr 23 answered On the degree of cyclotomic fields extension. Apr 23 comment Is there a category in which, between any two objects, there is a unique morphism? +1, agreed, not sure why you got a downvote. Apr 23 revised Is there a category in which, between any two objects, there is a unique morphism? edited title Apr 23 revised Is there a category in which, between any two objects, there is a unique morphism? added 237 characters in body Apr 23 revised Is there a category in which, between any two objects, there is a unique morphism? deleted 16 characters in body Apr 23 answered Is there a category in which, between any two objects, there is a unique morphism? Apr 22 revised Why does rotation by a quaternion require multiplying two times? added 8 characters in body; edited title Apr 22 reviewed Edit inverse of a root of f in an extension field K. Apr 22 revised inverse of a root of f in an extension field K. just notation Apr 22 revised Which cyclotomic fields are different? added 148 characters in body Apr 22 answered Which cyclotomic fields are different?