Intereting Posts

Is this a valid proof of $\lim _{n\rightarrow \infty }(1+\frac{z}{n})^n=e^z$?
How do you prove that proof by induction is a proof?
Are polynomials over $\mathbb{R}$ solvable by radicals?
Are there infinitely many rational pairs $(a,b)$ which satisfy given equation?
How to establish $\lim\limits_{r\rightarrow 0}\int_C f(z)dz=i\lambda(\theta_2-\theta_1)$?
Terminology re: continuity of discrete $a\sin(t)$
Simplifying factorials: $\frac{(n-1)!}{(n-2)!}$
Is this an outer measure, if so can someone explain the motivation
Let $p^k$ be the $p$-component of $a^t – 1$ i.e. $p^k\|a^t – 1$
Tensor product of reduced $k$-algebras must be reduced?
Properties of dual spaces of sequence spaces
Differentiate the following w.r.t. $\tan^{-1} \left(\frac{2x}{1-x^2}\right)$
Feeding real or even complex numbers to the integer partition function $p(n)$?
Express $u(x,y)+v(x,y)i$ in the form of $f(z)$
Find the ordinary generating function $h(z)$ for a Gambler's Ruin variation.

I feel intuitively that for $\prod_{i\in N}\mathbb{Z}$, as a $\mathbb{Z}$−module, and $\phi_i:\mathbb{Z}\to\mathbb{Z}$ the identity map, more than one homomorphism $\phi:\prod_{i\in N}\mathbb{Z}\to\mathbb{Z}$ satisfies the condition “composition with the canonical embedding yields the identity map $\phi_i:\mathbb{Z}\to\mathbb{Z}$”. But I can’t myself define such homomorphisms $\phi:\prod_{i\in N}\mathbb{Z}\to\mathbb{Z}$.

Could anyone suggest some appropriate functions?

- Infinite coproduct of rings
- Hom-functor preserves pullbacks
- Geometric intuition of tensor product
- Proving ring $R$ with unity is commutative if $(xy)^2 = x^2y^2$
- Centralizer of a given element in $S_n$?
- Proving that $\left(\mathbb Q:\mathbb Q\right)=2^n$ for distinct primes $p_i$.

- Confused on a proof that $\langle X,1-Y\rangle$ is not principal in $\mathbb{Q}/\langle 1-X^2-Y^2\rangle$
- Ring structure on subsets of the natural numbers
- Giving meaning to $R$ (for example) via the evaluation homomorphism
- Presentations of Semidirect Product of Groups
- nilpotent elements of $M_2(\mathbb{R})$, $M_2(\mathbb{Z}/4\mathbb{Z})$
- Single $\text{GL}_n(\mathbb{C})$-conjugacy class, dimension as algebraic variety?
- Product of two primitive polynomials
- In $R$, $f=g \iff f(x)=g(x), \forall x \in R$
- Prove that there is no element of order $8$ in $SL(2,3)$
- New discovery of the unconventional matrix representation for the quaternion $H_8$

It is a well-known result by Specker (original reference, MO/10239) that homomorphisms $\mathbb{Z}^\mathbb{N} \to \mathbb{Z}$ are determined by what they do on the $e_i=(\delta_{ij})_j$ and that almost all $e_i$ are mapped to zero. In particular, there is no homomorphism mapping all $e_i \mapsto 1$.

- Prove that $\prod_{k=1}^{n-1}\sin\frac{k \pi}{n} = \frac{n}{2^{n-1}}$
- Explicit example of Koszul complex
- How can I show that $\begin{pmatrix} 1 & 1 \\ 0 & 1\end{pmatrix}^n = \begin{pmatrix} 1 & n \\ 0 & 1\end{pmatrix}$?
- Yoneda-Lemma as generalization of Cayley`s theorem?
- Sum of n consecutive numbers
- An elementary functional equation.
- Prove by Induction: $8^n – 3^n$ is divisible by $5$ for all $n \geq 1$
- Condition on x-coordinate of a point such that three distinct normals can be drawn to a parabola
- Finding a third degree equation that fits two points with given slopes
- When does function composition commute?
- What is $\int x\tan(x)dx$?
- Is Every (Non-Trivial) Path Connected Space Uncountable?
- Example of $f,g: \to$ and riemann-integrable, but $g\circ f$ is not?
- Solving $(z+1)^5 = z^5$
- Is there another kind of two-dimensional geometry?