Example 1: There are 45 numbers 45 plus 1 is 46, then divide by 2 and you get 23 So the median is the 23rd number in the sorted list. Example2: There are 66 numbers 66 plus 1 is 67, then divide by 2 and you get 33.5 33 and a half? That means that the 33rd and 34th numbers in the sorted list are the two middle numbers. 发生过，近的远的都有。 远的是1994 年，当时美国经济过热，通胀抬头，美联储超预期连续加息 6 次，市场完全没做好心理准备。 结果不只是美国债市大跌，欧洲各国债券同步被抛售，全球债券市值大规模缩水。 核心是美联储激进加息预期，全球货币政策同步收紧。 近的是2022 年，全球大通胀债市. $\lambda =1$ is an eigenvalue corresponding to the eigenvector 1. Also when you try to diagonalize a stochastic matrix that all rows sum to 1 the characteristic polynomial will factor out (λ − 1) (λ 1) @turkeyhundt I don't like appealing to common sense results like this because it would lead one to believe that negative binomials (for example) aren't a thing due to the factorial function, and yet there is another definition that works (generalized version). I am after something a little more rigorous. The elementary but very useful inequality that 1 + x ≤ex 1 + x ≤ e x $1+x\le e ^ x $ for all real x x $x$ has a number of different proofs, some of which can be found online. But is there a particularly slick, intuitive or canonical proof? 三国群英传从1998年开始至今，历经7个版本，还有两部网游，在资深玩家心中，哪个版本最经典，最耐玩？说… The technique is useful in computation, because if the values in A and B can be very different in size then calculating 1 A+B 1 A + B $\frac 1 A+B $ according to (3) (3) 知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。 $1= 1 ^ 2 = 1 ^ 3 =\cdots$, so that the 0 0 $0$ is a redundant symbol. The use of it in the unary system does not make it binary. That statement, as well as the following one that there is no explicit symbol for 0 0 $0$, is sensible only under the presumption that base-representations of natural numbers should be bijective. There may certainly. Factor out the n n $n$ using given identity and adjust the remaining sum so that you can use the known sum of binomial coefficients.