The power of linearity is F=k1+k2 if I come across f of x, y, z equals k1 plus k2, if it is a linear equation, I don't have to go and solve it all over again.
线性的威力是,一个方程,如果它是个线性方程,那么我就不用再去解他了。
Two plus one equaled three before there were people; two plus one equals three now; two plus one will always equal three.
在人类出现之前,二加一就等于三,二加一现在等于三,并将永远等于三
pV=RT p plus a over v bar squared times v bar minus b equals r t. All right if you take a equal to zero, these are the two parameters, a and b. If you take those two equal to zero you have p v is equal to r t.
我们就回到,也就是理想气体,状态方程,下面我们来看看,这个方程。
System of linear equations. What are the equations here? Well, I could say, you know, the number of pigs plus the number of 20 chickens equals 20, right? Because we've got 20 heads. And then what else do I have?
如何解决这个问题呢?,用线性方程式的办法来解决,等式是什么呢?你应该知道,猪的数量加鸡的数量等于,对吧?因为我们有20个头?
And the mathematics of that equation involved a double derivative in time of x 0 plus some constant times x equals zero with some constraints on it.
那个数学方程式,包括了x对时间的二阶导数,加上常数乘以x等于,还有一些限制条件。
So similarly, I would find that ?2 2 equals 1 plus B S1 and this is the best response of Player II, as it depends on Player I's choice of effort S1.
同理可得?2等于1+B*S1,?2是参与人II的最佳对策,因为它与参与人I的策略S1有关
It's as though you try-- try getting upset about the fact that two plus two equals four.
这就像你在尝试-,为二加二等于四而烦恼。
So he curses existence, curses God at having made him so impotent that he can't change the fact that two plus two equals four.
所以他诅咒生存,诅咒上帝让他如此无能,无能到无法改变二加二等于四的事实。
Try feeling upset at your powerlessness to change the fact that two plus two equals four.
尝试为你无力,改变二加二等于四的事实而痛苦。
And so he imagines that God, as omnipotent, could've made two plus two equals five.
所以他猜想,万能的上帝可以让二加二等于五。
It will still be true that 3 plus 1 equals 4.
加1仍然等于。
We are able to talk about the fact that two plus one equals three, but it's not as though we ever come across numbers-- number three itself--anywhere in the empirical world.
我们可与去探讨,二加一等于三的这个事实,但是我们不可能有一天真的碰到数字,在现实世界中碰到个叫"数字三"的东西
Three plus one equals four, today, yesterday and forever.
加1等于,昨天是今天是永远都是。
We all do believe something makes it true that two plus one equals three, but it's not the fact that empirical objects-- We don't do empirical experiments to see whether two plus one equals three.
我们都相信有些东西,使2加1等于3是正确的,但这不是说现实的东西,我们不会在现实中做实验,去看看二加一是不是等于三
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