Almost all books teach Law of Large Numbers first then the Central Limit Theorem one next. But what are the relationship and differences between two theorem?
Here is my understanding (Informally),
Law of Large Numbers says if we have very large i.i.d sample, the mean will converge to a number.
Central Limit Theorem is similar idea, but require "less data" (I agree with Tim in the comment that both refer to $\infty$, but I cannot find a better word to describe..). Comparing to Law of Large Numbers, because it require "less data", it has a relaxation in conclusion: not converge to a number, it converge to a normal distribution.
Thanks for Yuri and Antoni's links, I think my question is different from the two questions linked.
It focusing on more math, where I want more "intuitive explainable" on application domain or the scope on LLN and CLT, but not only the math derivation.
It is closer to what I want to ask, but still focusing on "how then can CLT also converge to the expected value at the same time?"