general
Common inadequate definitions
I had the good fortune of assigning the following problem on the first day of my freshman honors calculus course: Is $a$ contained in the interval $[a,a)$...
Apr 12, 2026
Archive: General
general
What is a regular FG-module?
What is meant by a regular $FG$-module. $G$ is a group and I believe $F$ is supposed to be a field. I'm completely confused by this concept on a ques...
Apr 12, 2026
general
Proofs involving multiple quantifiers?
I'll just give this simple example to illustrate my point: There exists a real number $x$ such that for every real number $y$, we have $xy=y$. If I w...
Apr 11, 2026
general
Alternating Series Estimation Theorem and this series
$$\sum_\limits{n=1}^\infty\frac{(-1)^{n+1}}{n^6}$$ With the error being $\vert \mathbf{error} \vert \lt \ .00005$ In order for the series to undergo the A...
Apr 11, 2026
general
Understanding the meaning of Unique Solution
General definition of System of Linear Equations says that "If The system has a unique solution, It has independent set of Equations" Consider the system ...
Apr 11, 2026
general
Independent Events happening at the same time
I'm trying to wrap my head around a pretty basic concept. But I'm not 100% sure my reasoning is right. I have an event that happens 10 times, at...
Apr 11, 2026
general
Applications of Abstract Algebra to elementary mathematics
I'm currently an undergraduate student in mathematics. I am currently taking Algebra. The course is interesting, but I have grown very curious about ...
Apr 11, 2026
general
Number of 5-regular graphs
I have to find a number of 5-regular non isomorphic graphs with 8 vertices. I just want to check if the answer is 2? My logic is to draw cycles $C_5+C_3$ ...
Apr 11, 2026
general
Computing the integral of $\log(\sin x)$
How to compute the following integral? $$\int\log(\sin x)\,dx$$ Motivation: Since $\log(\sin x)'=\cot x$, the antiderivative $\int\log(\sin x)\,dx$ h...
Apr 11, 2026
general
integrating complex functions
I need to integrate $$\int\limits_0^{\frac{\pi}{2}} e^{t+it} dt$$. This is equal to $\int\limits_0^{\frac{\pi}{2}} e^t \cdot e^{it} dt$ However I'm n...
Apr 11, 2026
