平凡,平凡解

多年来被这样一个词所困扰,就是平凡.
维基百科给出了非常好的解释:
我总结一下,"平凡"表示"连傻逼都知道的结论".
所以说做一个平凡的人就是做一个连傻逼都会做的人.但是这其实也不容易.

    In mathematics, it is often important to find factors of an integer number N. Any number N has four obvious factors: ±1 and ±N. These are called "trivial factors". Any other factor, if any exist, would be called "nontrivial".[1]
    数学里,一个数的因子,1和它自己总是它的因子,所以这些因子足够傻逼,而其他的则不那么好找,其它的就是不平凡的.

    The matrix equation AX=0, where A is a fixed matrix, X is an unknown vector, and 0 is the zero vector, has an obvious solution X=0. This is called the "trivial solution". If it has other solutions X≠0, they would be called "nontrivial"[2]
    AX=0的方程,很显然对于随便的A,X=0时有个解,所以连傻逼都一定知道X=0是解,所以这个0解是平凡的.其他解则是不平凡的.

    In the mathematics of group theory, there is a very simple group with just one element in it; this is often called the "trivial group". All other groups, which are more complicated, are called "nontrivial".
    群理论:如果一个群只有一个元素,也就是说这一个玩意就是一个群,这是一个多么傻逼的说法,所以它是平凡的.如果真的有一群,也就是多于一个的构成的群,才是非平凡的群.

    Mathematics has a concept called functional dependency, written X->Y. It is obvious that the dependence X->Y is true if Y is a subset of X, so this type of dependence is called "trivial". All other dependences, which are less obvious, are called "nontrivial".
    可以看成是命题吧,如果X,则Y,对于这个关系,如果Y是X的一个子集,傻逼都知道这个命题总是真的.
比如说X=(要加薪做了一些事,要加薪杀了人)->Y=(要加薪杀了人),因为Y是X的子集,所以这个命题傻逼都知道是真的.
推论:认为这个命题是假的的人处于(-无穷,傻逼)的开区间上.

    The differential equation f''(x) = − λf(x) with boundary conditions f(0) = f(L) = 0 is important in math and physics, for example describing a particle in a box in quantum mechanics, or standing waves on a string. It always has the solution f(x) = 0. This solution is considered obvious and is called the "trivial" solution. In some cases, there may be other solutions (sinusoids), which are called "nontrivial".[3]
    微分方程,f''等于f乘一个数,如果f(x)=x的任意次方,那么在零点的任意阶导数都是0,所以这个0点的解是傻逼的(平凡的).本问题没什么亮点.