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Math137's user avatar
Math137
  • Member for 11 years, 2 months
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6 votes
Accepted

The limit : $ \lim _{x \to \infty } \sqrt{x^2 +x} - \sqrt{x^2 +1} $

5 votes
Accepted

Does $\lim_{y \to 0} [\lim_{x \to 0} f(x, y)] \ne \lim_{x \to 0} [\lim_{y \to 0} f(x, y)] \implies \text{ no limit }$ works in the opposite direction?

4 votes
Accepted

Does it make sense to compare complex numbers in certain circumstances?

4 votes
Accepted

$G=\bigcup\limits_{i=1}^ \infty G_i$ and $G_n \subset G_{n+1} , \forall n \in \mathbb N$ $\implies$ $G$ is not cyclic

4 votes

Isomorphism in certain groups.

4 votes

Showing that $\lim_{n \rightarrow \infty} \left( 1 + \frac{r}{n} \right)^{n} = e^{r} $.

4 votes
Accepted

Proof of sum results

4 votes

Show that $(A / \mathfrak{a}) \otimes_A M \cong M / \mathfrak{a} M$ for a ring $A$, ideal $\mathfrak{a}$, $A$-module $M$.

3 votes

Accumulation point(s) of $\mathbb{R} \setminus \mathbb{N}$ in $\mathbb{R}$

3 votes

inverse of the square matrix

2 votes
Accepted

Quotient of noncommutative algebra

2 votes

Positive and negative complex numbers?

2 votes
Accepted

The automorphism group of a fixed field

2 votes
Accepted

Definition of Real Absolute Value

2 votes

Finding eigenvalues of given matrix

2 votes

Prove no real number satisfies $x^{2} = -1$

2 votes

Evaluate the integral $\int_0^{\ln(2)} \sqrt{(e^x-1)}dx$

2 votes
Accepted

Tensor product of modules and being torsion-free

2 votes

Tensor product of two $R$-modules

1 vote

$R$ Noetherian, $M$ finitely generated module. If $P$ is minimal over $\operatorname{ann}M$, how is $M' = \ker (M \to M_P)$ a $P$-primary submodule?

1 vote
Accepted

Proof exercise on the topic of eigenvalues

1 vote

Verify that R is a ring

1 vote

How do I find which set of functions is linearly independent?

1 vote
Accepted

$M\simeq D$ and $N\simeq D$ then $M\oplus N\simeq D\oplus D$?

1 vote
Accepted

When is $M\otimes N$ a module?

1 vote

limit of rational sequence

1 vote
Accepted

Short Exact Sequences

1 vote
Accepted

Quasi-hereditary algebras

1 vote

Solution Set of $\sqrt{x+1}+\sqrt{x-1}=1$

0 votes

Is Quotient Ring algebraic