Prove or disprove that the sum of two irrational numbers is irrational [duplicate]
Prove or disprove that the sum of two irrational numbers is irrational. How do i answer this? Thanks.
Apr 11, 2026 1 VIEWS
Topic: General
5104 Articles 
Find homoclinic bifurcation points
given the following simple system $$ \dot{x}=x\left(1-ax-\frac{y}{1+x^2}\right)\\ \dot{y}=y\left(b\frac{x}{1+x^2}-c\right) $$ I am trying to produce a thr...
Apr 11, 2026 1 VIEWS
How to convert into a definite integral
Could you show me how to convert the following into a definite integral: $$\lim\limits_{n \to \infty} \sum_{k=1}^{3n} \frac{1}{n}\cos\left(\frac{k\pi}{n}\...
Apr 11, 2026 1 VIEWS
Properties Of Modulo
I am just starting with competitive programing and usually numbers get way too large so we tend to work with $$ \mod 10^9+7$$ I am familiar with some prop...
Apr 11, 2026 1 VIEWS
Prove the limit of $\cos(1/x)$ does not exist as $x \to 0$, by using Epsilon and Delta.
I was trapped by this question at least for two hours. I negated the definition of limit first, and then try to prove $$\lim_{x \to 0}\cos\left(\frac1x\ri...
Apr 11, 2026 1 VIEWS
Is it impossible to grasp Multivariable Calculus with poor prerequisite from Single variable calculus? [closed]
Would it be possible to keep up or would i be overwhelmed by a hopeless struggle trying to grasp the new material while at the same time looking back at a...
Apr 11, 2026 1 VIEWS
Laplace transform of a square wave function
What is the right way to find the Laplace transform of this function: The thing I noticed was: $$f(t)=\text{A}\space\space\space\space\space\space\space\s...
Apr 11, 2026 1 VIEWS
Calculator will not find row reduced echelon form
I have a TI-84 Plus CE which I am using to find the row reduced echelon form of matrices. It has worked well so far, but it gives me an "Invalid Dimension...
Apr 11, 2026 1 VIEWS
Finding tangent vector for a curve at a given point
For a problem like this where I have to find the tangent vector at the point $(0,0,1)$: $$r(t) = \sin(t)i + (t^2 − t)j+\sqrt{1 + t}k$$ I know I would take...
Apr 11, 2026 1 VIEWS
What does "$\cong$" sign represent?
I came across this sign when reading some papers. I looked up Wikipedia. It says "The symbol "$\cong$" is often used to indicate isomorphic algebraic stru...
Apr 11, 2026 1 VIEWS
How to calculate percentage of value inside arbitrary range?
So pardon if this is a simple question... I have a slider that returns a value in a given range, so: min: 174 max: 424 slider current value: 230 I want to...
Apr 11, 2026 1 VIEWS
How do I derive the center of the symplectic group?
I define the real symplectic group to be the set of $2n \times 2n$ matrices satisfying \begin{equation} S\Omega S^\intercal = \Omega, \end{equation} where...
Apr 11, 2026 1 VIEWS