2016-10-07

beautify i3wm

MotivationI enjoy using i3wm, big time. You can switch to different windows/apps conveniently with it. The only problem to me is that it’s not beautiful enough, and it’s ridiculously small in my high-

Math

2016-10-06

The empty set is the subset of any set

The empty set is the subset of any set. This is true. Some people take it as a convention, but in fact, it can be explained. According to the definition of $\subset$, $\varnothing\subset A\Leftrighta

Math

2016-10-01

Understand poisson distribution

IntroductionPoisson distribution can be derived from Binomial distribution when $\lim\limits_{n\to\infty}np = \lambda(\lambda\in\mathbb R)$, in which $n$ is the number of trials, $p$ is the probabilit

Math

2016-10-01

Proof of $$\lim_{x\rightarrow \infty} f(x)^{g(x)} = c^d$$

Theorem: $$c,\ d\in {\bf R},\ \lim_{x\rightarrow \infty} f(x)=c>0,\ \lim_{x\rightarrow \infty} g(x) =d>0$$ then $$\lim_{x\rightarrow \infty} f(x)^{g(x)} = c^d$$ Proof: Because $y(x)=ln(x)$ i

Coding

2016-10-01

Let hexo support mathjax

UpdateThe original answer fails on some mathjax expressions. So don’t use it. Currently changing marked.js works for me. Just use the method below. It works for me. First introduce mathjax into our bl

Math

2016-10-01

Proof of the limit's composition law when x approaches infinity

Theorem: If $f(x)$ is continous at $b$ and $\lim\limits_{x \to\infty}g(x) = b$, then $$\lim\limits_{x \to \infty}f(g(x)) = f(b) = f(\lim\limits_{x\to \infty}g(x))\tag1$$ Proof: Because $f(x)$ is con

Archive: 2016/10

beautify i3wm

The empty set is the subset of any set

Understand poisson distribution

Proof of $$\lim_{x\rightarrow \infty} f(x)^{g(x)} = c^d$$

Let hexo support mathjax

Proof of the limit's composition law when x approaches infinity