If $x$ and $y$ are irrational, is $x + y$ irrational? Is $x - y$ irrational?

The equation is $$\frac{1}{5} - \frac{3}{x},$$ rewritten as $$\frac{1}{5} - 3x^{-1}.$$ So the anti-derivative should be $$\frac{1}{5}x - 3\frac{x^0}{0} + ...

This is my first proof related to linear functions. It refers to the linear-algebra-$\textit{linear}$ (not the calculus-$\textit{linear}$). Please comment...

I am recently learning from Loring W. Tu's An Introduction to Manifolds the concept graded algebra, which is used for introducing exterior algebra. I...

I was given this problem: Find an integral equal to the volume of the solid bounded by $z=4-2y,z=0,x=y^4,x=1$ and evaluate. I understand how to evaluate o...

The perimeter of a square is 48 inches. What would be the length, in inches, of its diagonal?

Find the limit of $\frac{4x^4 + 5y^4}{x^2 + y^2}$ as $(x,y)\to (0,0)$. Which method do I use to find the limit of that? I tried paths but the limits all c...

Given the IVP $$ y'' + y = f(t) , \qquad\quad y(0) = 0 , \quad y'(0) = 0 , \tag{1}$$ where $$ f_{k} (t) = u_{0} + 2 \sum_{k=1}^{n} (-1)^{k}...

How can I fully understand what are conjugacy classes are in groups? I know the definition, that $a$ and $b$ are conjugate if $gag^{-1}=b$ for some $g\in ...

Are there any really good non linear regression calculators around the web? Or is something like MATLAB the best solution? I tried using excel and its sol...