Intereting Posts

Can I understand Egorov's theorem in this way?
Is $f_n$ uniformly convergent on $(0,\infty)$?
What is the next “Tribonacci-like” pseudoprime?
Spectrum of a Self-Adjoint Operator is Real
Fastest way to check if $x^y > y^x$?
Number-theoretic asymptotic looks false but is true?
Deriving equations of motion in spherical coordinates
Intersection of compact and discrete subsets
Number of nonnegative integer solutions to $x_1+x_2+x_3\le10$ with $x_1 \ge 1\ ,\ x_2\ge3$
Determine $x$ such that $\lim\limits_{n\to\infty} \sqrt{1+\sqrt{x+\sqrt{x^2…+\sqrt{x^n}}}} = 2$
Does $\sum a_n$ converge if $a_n = \sin( \sin (…( \sin(x))…)$
Calculating the limit of $^{1/n}$ as $n$ tends to $\infty$
Fibonacci numbers and proof by induction
“Proof” that $1-1+1-1+\cdots=\frac{1}{2}$ and related conclusion that $\zeta(2)=\frac{\pi^2}{6}.$
How to construct a function from a pair of possibly empty sets?

Not sure where to go with this, but I don’t think it is cyclic..

- Neat way to find the kernel of a ring homomorphism
- Prove that G is a cyclic group
- Isomorphism from $B/IB$ onto $(B/I)$
- Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian
- Is normal extension of normal extension always normal?
- Show that $\Bbb Q(\sqrt{a}, \omega )=\Bbb Q(\sqrt{a}+ \omega )$
- Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.
- book with lot of examples on abstract algebra and topology
- Prove Principal Ideal Domain from Bezout's condition, and terminating divisibility chain
- Subgroups of symmetric group

Hint: supose $\;m,n\in\Bbb Z\;$ are such that $\;\Bbb Z\times\Bbb Z=\langle (m,n)\rangle\;$, then among other things there must exist $\;x\in\Bbb Z\;$ s.t.

$$x(m,n)=(1,1)\implies xm=1=xn\implies\ldots ?$$

Well, now it must **also** be true that there exists $\;y\in\Bbb Z\;$ s.t. :

$$y(m,n)=(0,1)\implies ym=0\;,\;yn=1$$

So…

Suppose it were cyclic, with generator $(a,b)$. Then every element of ${\mathbb Z} \times {\mathbb Z}$ would have to be of the form $(na,nb)$ for some $n \in {\mathbb Z}$. Can that occur?

- What are some good math specific study habits?
- $\operatorname{MaxSpec}(A)$ closed
- How to put 9 pigs into 4 pens so that there are an odd number of pigs in each pen?
- Derivation of Gradshteyn and Ryzhik integral 3.876.1 (in question)
- Why is $|Y^{\emptyset}|=1$ but $|\emptyset^Y|=0$ where $Y\neq \emptyset$
- Value of $\sum 1/p^p$
- Probability of two people meeting in a given square grid.
- probability distribution of coverage of a set after `X` independently, randomly selected members of the set
- Find the minimum value of $P=\sum _{cyc}\frac{\left(x+1\right)^2\left(y+1\right)^2}{z^2+1}$
- Is there an algebraic homomorphism between two Banach algebras which is not continuous?
- Continuous local martingales with same crochet have the same law?
- Prove variant of triangle inequality containing p-th power for 0 < p < 1
- Does the proof of Bolzano-Weierstrass theorem require axiom of choice?
- Prove that $A+B=-2I_{4}$
- Best book for topology?