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Mathematics Stack Exchange
Q&A for people studying math at any level and professionals in related fields
Newest Questions - Mathematics Stack Exchange
Mathematics Stack Exchange is a platform for asking and answering questions on mathematics at all levels.
notation - Difference between "≈", "≃", and "≅" - Mathematics Stack ...
In mathematical notation, what are the usage differences between the various approximately-equal signs "≈", "≃", and "≅"? The Unicode standard lists all of them inside the Mathematical Operators B...
(Un-)Countable union of open sets - Mathematics Stack Exchange
A remark: regardless of whether it is true that an infinite union or intersection of open sets is open, when you have a property that holds for every finite collection of sets (in this case, the union or intersection of any finite collection of open sets is open) the validity of the property for an infinite collection doesn't follow from that. In other words, induction helps you prove a ...
Prove that that $U (n)$ is an abelian group.
Prove that that $U (n)$, which is the set of all numbers relatively prime to $n$ that are greater than or equal to one or less than or equal to $n-1$ is an Abelian ...
For what $n$ is $U_n$ cyclic? - Mathematics Stack Exchange
When can we say a multiplicative group of integers modulo $n$, i.e., $U_n$ is cyclic? $$U_n=\ {a \in\mathbb Z_n \mid \gcd (a,n)=1 \}$$ I searched the internet but did ...
Limit sequence (Un) and (Vn) - Mathematics Stack Exchange
Limit sequence (Un) and (Vn) Ask Question Asked 9 years, 5 months ago Modified 9 years, 5 months ago
Carleman Estimates - Mathematics Stack Exchange
I'm looking for the article Carleman, T. Sur un problème d'unicité pur les systèmes d'équations aux dérivées partielles à deux variables indépendantes. (French) Ark. Mat., Astr. Fys. 26, (1939). ...
$\operatorname {Aut} (\mathbb Z_n)$ is isomorphic to $U_n$.
(If you know about ring theory.) Since $\mathbb Z_n$ is an abelian group, we can consider its endomorphism ring (where addition is component-wise and multiplication is given by composition). This endomorphism ring is simply $\mathbb Z_n$, since the endomorphism is completely determined by its action on a generator, and a generator can go to any element of $\mathbb Z_n$. Therefore, the ...
Is zero odd or even? - Mathematics Stack Exchange
Some books say that even numbers start from $2$ but if you consider the number line concept, I think zero($0$) should be even because it is in between $-1$ and $+1$ (i.e in between two odd numbers)...
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