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 Feb13 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 ${-1,1}$. Feb13 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 $x$? Feb13 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? Feb13 awarded Organizer Feb13 revised Mapping Proof Abstract Algebra (HW) Replaced abstract-algebra tag with set-theory Feb13 suggested approved edit on Mapping Proof Abstract Algebra (HW) Feb13 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? Feb12 revised $a_{n}b_{n} \rightarrow 0$ if $(a_{n})$ is bounded and $(b_n)$ converges to $0$ TeX'd the question. Feb12 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 $\alpha \in M$. Feb12 suggested approved edit on $a_{n}b_{n} \rightarrow 0$ if $(a_{n})$ is bounded and $(b_n)$ converges to $0$ Feb12 awarded Editor Feb12 revised If I wanted to show that an isometry is always continuous, is this right? added 38 characters in body Feb12 answered Induction: prove using congruences Feb12 awarded Citizen Patrol Feb12 answered A statement true about compacts but false about closed sets Feb12 awarded Supporter Feb12 answered If I wanted to show that an isometry is always continuous, is this right? Feb12 awarded Teacher Feb12 answered What is the difference between half space and hyper plane? Feb12 answered probability and combinations