V3 Here's the V4 over V3, V1 oops, sorry. V2 over V1, this is equal to the inverse of this.

所以就是这里的V4除以，哦，对不起，V2除以，它是它的倒数。

麻省理工公开课 - 热力学与动力学课程节选

Here's what I do. I change-- oops! Let me do that this way-- I change last to here, and keep first there, and I throw away all of that. All right?

接下来，我来改过来,此时这里是last，first位置没变,把这些都擦掉，好？

麻省理工公开课 - 计算机科学及编程导论课程节选

On the next step though, this, we get substituted by that. Right, on the next step, I'm back in the even case, it's going to take six more steps, plus t of b minus 1. Oops, sorry about that, over 2.

这一步就是偶数了，这一步会让我们得到，6+t这样的结果，因为b-1现在是偶数了,别忽略这里的细节。

麻省理工公开课 - 计算机科学及编程导论课程节选

It's gonna happen wrong, and the guy's gonna be late because his dog got run over, and he's going to fix the wrong pipe, and when he takes it apart he's gonna say, 'Oops, the whole plumbing system's gonna have to go and dah dah dah and etc. etc. etc.

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