TIL that if it took a spaceship one second to travel Earth's diameter, it would take the same spaceship nearly two days to travel the diameter of the largest star we know of
@TobiasKildetoft couldn't you take the reals under addition, and then double the point $0$, say, adding $0'$. Make $0'$ the left and right identity for $1$ and $-1$, and $0$ the identity for everything else...
@ForeverMozart Suppose I have a locally compact, Hausdorff, second countable space $X$. I want a sequence of open sets $\{K_i\}$ with compact closure, such that $\bar K_i\subset K_{i+1}$ and they cover $X$.
Hi. Off topic probability: "Let $I$ be uniform on $\lbrace 1,\ldots, n\rbrace$, $(X_1',\ldots,, X_n')$ be an independent copy of $(X_1,\ldots, X_n)$..." What does it mean to be an independent copy? That sounds absurd to me.
Can someone post the link that's needed to render formulas in here?
Well, anyway, I was trying to render LaTeX but I'll do that later since my browser seems to be running into other problems. Hopefully the little LaTeX I've written is rendering correctly.
A system ("A System is any physical set of components that takes a signal, and produces a signal") is described by this equation:
$ \frac{dy(t)}{dt} + 3 \times y(t) = x(t) $
Where $x(t)$ is the input and $y(t)$ the output.
How to determine if this system is a linear one?
maybe the equation came from something, or is intended to mimic situations where you have mixtures of letters because reasons
generally when you have an ODE, if you want to think of it as operator(function)=function, the input function is the thing with derivatives appearing and the output function is the thing on the other side of the equation
A system ("A System is any physical set of components that takes a signal, and produces a signal") is described by this equation:
$ \frac{dy(t)}{dt} + 3 \times y(t) = x(t) $
Where $x(t)$ is the input and $y(t)$ the output.
How to determine if this system is a linear one?
