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 Feb 13 comment Bound on sum of $x$ independent uniform random variables. Okay. I'm not sure how Chernoff would help you here since $D_{i}$ are not binary or in ${-1,1}$. Feb 13 comment Bound on sum of $x$ independent uniform random variables. If we take $x=1$ then $Pr(D \leq \frac{n}{4}) \approx \frac{1}{4}$, no? Is there some condition on $x$? Feb 13 comment If G is a finite group with an even number of elements, then binary product of two distinct elements is identity. Well, you know that $ee=e$, and each $g \in G$ has a unique $g^{-1} \in G$. Can you see a way to continue from here? Feb 13 awarded Organizer Feb 13 revised Mapping Proof Abstract Algebra (HW) Replaced abstract-algebra tag with set-theory Feb 13 suggested approved edit on Mapping Proof Abstract Algebra (HW) Feb 13 comment Mapping Proof Abstract Algebra (HW) @Lilluda5 start with what you're given. Assume that $f:S \rightarrow S$ is one-to-one but not onto. Can you construct a $g:S \rightarrow S$ from $f$ that is onto? Feb 12 revised $a_{n}b_{n} \rightarrow 0$ if $(a_{n})$ is bounded and $(b_n)$ converges to $0$ TeX'd the question. Feb 12 comment If I wanted to show that an isometry is always continuous, is this right? I think you might be confused about metrics. $d_{M}(p,q) \in \mathbb{R}$ by definition. $M$ is some metric space, and not necessarily $\mathbb{R}$, so you can't say that $\alpha \in M$. Feb 12 suggested approved edit on $a_{n}b_{n} \rightarrow 0$ if $(a_{n})$ is bounded and $(b_n)$ converges to $0$ Feb 12 awarded Editor Feb 12 revised If I wanted to show that an isometry is always continuous, is this right? added 38 characters in body Feb 12 answered Induction: prove using congruences Feb 12 awarded Citizen Patrol Feb 12 answered A statement true about compacts but false about closed sets Feb 12 awarded Supporter Feb 12 answered If I wanted to show that an isometry is always continuous, is this right? Feb 12 awarded Teacher Feb 12 answered What is the difference between half space and hyper plane? Feb 12 answered probability and combinations