# Tagged Questions

For questions concerning a specific proof, asking for verification, identifying errors, suggestions for improvement, etc.

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### Use the definition of a limit to prove that $\lim_{y \to 0} y^3 = 0$.

Attempt: The limit $\lim_{y \to 0} y^3 = 0$ exists if: $$\forall\ \epsilon >0 \ \exists\ \delta >0 \ \forall y \ |y-0| < \delta \Longrightarrow |y^3 - 0|< \epsilon.$$ Now, I came up ...
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### proof - Bézout Coefficients are always relatively prime

I had been researching over the Extended Euclidean Algorithm when I happened to observe that the Bézout Coefficients were always relatively prime. Let $a$ and $b$ be two integers and $d$ their GCD. ...
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### Find the inverse of the following piecewise defined function

Find the inverse of $f$ if $f(x)=$ $$\begin{cases} \sqrt{2-x}, &\text{for x<0}\\ 1-x^2, &\text{for x \ge 0} \\ \end{cases}$$ My effort For $y=\sqrt{2-x}$ ,we find \begin{array}{...
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### Is the following proof of $Z(S_n)=\{id\}$ correct?

I wanted to prove that the center of the symmetric group $S_n$, $n\geq 3$ is trivial. Is my argument correct? Suppose $\alpha\in Z(S_n)$, that is $\alpha\beta=\beta\alpha$ for all $\beta\in S_n$. We ...
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