# Tag Info

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### Is this a valid proof that a subset of $\mathcal{L}(V, W)$ is not closed under addition

Okay, at this point there's slightly too much to say to fit into the comments so I'll convert them into an answer. This is heading in the right direction (you want to show that $S$ is not closed ...
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### Solution-verification: Solve $3x^2-6x+4 = 6\{x\}\bigl(\lfloor x\rfloor - \{x\}\bigr)$

I think it's accepted that the algebraic calculations once you substitute $x=a+b$ are valid so let's talk about why you can make this substitution. Most steps in solving equations are "if and ...
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Accepted

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1 vote
Accepted

### Precisely sketch the mapped region and write the equations of its boundaries.

This region is a triangular region with vertices at $0$, $1$, and $-1$. This is not correct. The vertices are at $i$, $1$ and $-1$. jjagmath has already provided a good geometric answer. So, in the ...
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Accepted

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1 vote

### Redundancy in the definition of uniform spaces

No. If you take $\Phi = \{\Delta\}$, it satisfies Definition B. However, it is not a uniformity.
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1 vote

You have the right idea, but you are overcomplicating things. You don't need Thm 2, for example. Assume that for each $i$, there is some $i$ for which $x^d_i\in\mathfrak{a}$. Then, for all $m_i\geq ... • 15.3k 1 vote Accepted ### Let R be a ring with three elements. Show that$x^2=y^2$if$x,y$are non-zero elements of R. To spell out CJ Dowd's comment: if$R$is any ring, then let$\lambda\colon R \to \text{Hom}_{ab}(R,R)$(where target of$\lambda$is the ring of group homomorphisms from the additive group of$R$to ... • 5,123 1 vote ### Find$\displaystyle\lim_{n \to \infty} \int_0^\infty \frac{1+\frac{x}{\sqrt{n}}e^{-x/n}}{(x+1)^2} \, dx$Since there are different scales at play ($\sqrt{n}$and$n$) in this kinds of situations is often useful to split the integral in intervals that grow as$n\rightarrow\infty\$ and/or use the following ...
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