I had to show that, when given two numbers, $a\in\Bbb{R}\text{\\}\Bbb{Q}, b\in\Bbb{Q}$, $a+b$ is irrational. I tried Reductio ad absurdum, and assumed $a+b\in\Bbb{Q}$. Then, I assigned $a+b$ to $c$, whereas $c\in\Bbb{Q}$. $\implies a=c-b, c-b\in \Bbb{Q}$, $a\in\Bbb{R}\text{\\}\Bbb{Q}$, which obviously leads to a contradiction. This implies that $a+b\in\Bbb{R}\text{\\}\Bbb{Q}$. Is this proof correct?
@LeakyNun I was chided by two people on the main site for providing an answer that pointed out the bad parts of a proof, while the other answer that simply said the proof was well done got many upvotes. This is one reason I will no longer have an account here.
my understanding of Asian people is they look mid 20's until 30 years later then they magically look 50 and some time later they magically jump from looking 50 to looking 1000 +
@Jasper sorry to hear about your health. There's nothing worse than being ill, and we all take our health for granted at some point or another. I sincerely hope you overcome your sickness.
@Dodsy Last year when I went out, some girl asked me for donations for a charity. And she said 'Don't you have school today?' She thought I was 16, lol.
@LeakyNun but I knew you asked about pinyin because I saw "pinyin ma?" ma is just basically question mark isn't it? and I knew what pinyin was :D. I really have a limited understanding of Mandarin, probably better at German. My native language is English.
"Frisch weht der Wind, der heimat zu? Mein Irisch Kind, wo weilest du?" I barely know what the individual words mean, but I know what that sentence means/what it's a reference to
For example, the "t" in parametric equations for curves would be an example of a parameter. It is the input to the function that maps the t values to n-dimensional coordinates.
@BalarkaSen Typical ODEs are deterministic, in that there is no "noise" to consider; with appropriate initial/boundary conditions, your solution is determined by the equation.
In stochastic ODEs, part of your DE is a stochastic process--think Brownian motion for example--and its solution will also be a stochastic process. There's noise to consider.
