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 $T(z)=1/z$. Find the image of $y=2x+1$ under $T$. I assume x and y are the real and imaginary part of Basically what I need was let $w=1/(x+(2x+1)i)$ then multiplied by the complex conjugate we have that the real imaginary part of x. We have $$w=\frac{x}{x^2+(2x+1)^2}+\frac{(2x+1)}{x^2+(...

I propose creating a tag gauge-integral. (Perhaps also with synonym henstock-kurzweil-integral.) There are some questions on the main site about this type of integral. Perhaps not that many, but it seems that some users are interested in this topic. However, searching for questions concerning g...

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...