Consider an $n$-vertex directed graph $G = (V, E)$ with the property that every vertex has an edge into it. That is, for each $v \in V$, we have that $(u,v)$ is in $E$. I define a dominating set $D \subseteq V$ for $G$ to have the property that for all $v \in V$, either $v \in D$ or $(u,v) \in E$...
Let $X$ be a random variable. Is there a way to bound the probability that $|X|$ is large in terms of $\Bbb{E}(X^{4})$?
I am reading Rudin's Principles of Mathematical Analysis in order to prepare for my first course in Real Analysis I intend to take this fall. The book just defined what an upper bound is and then defined supremum/ least upper bound as: Suppose $S$ is an ordered set, with $E$ as a subset of $S...
Let $a\in\mathbb{N}$. is there an upper bound be for the smallest n so that $n!>a$? It doesn't have to be a good upper bound, just something that works. Thanks.
I'm self studying real analysis. I know I can find this proof easily on the internet, but I want to learn from my mistake. Can anyone tell me if my proof is correct or point me where is incorrect. thank you. Proove that if $b^0$ = supremum E, then $b^0$ is unique Suppose that $b^0$ is the sup...
Resolved: Both tags have been manually removed. I recently noticed two new tags upper-bound and lower-bound. AFAICT both were first used in August 2016 in this post. Currently there are about 20 questions carrying either tag. Neither has a tag wiki nor a follower. The topics of the question...
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