>In article <email@example.com>, >Anonymous wrote: >>David: >> >>>Actually from what you say here it seems pretty likely that >>>you do know what linear independence _is_, but the >>>way you're stating the definition is totally wrong. >> >>Right. That's my point. I *do* know the definition, but the phrasing always >>gets me. > >That tells me that you do not really "know" the definition. You >->think<- you know it, you ->think<- you understand it, but you >actually do not. If you did, the phrasing would not be a problem.
Or, as seems quite possible from the definition he gave, he does understand what independence means, but he doesn't understand how to state things coherently. (Which of course is equally fatal - one of many reasons for memorizing these definitions vergatim is to give us a stock of examples to use in learning _how_ to say _exactly_ what we mean.)
>> It's like this, probably, for a bunch of the main terms. Still, you >>say the number one problem is that students don't understand all the >>definitions. Is my understanding of "independence" then not good enough? Or >>is it? > >If your understanding is not sufficient to lead you to a coherent and >correct statement of the term, then it is not good enough. Unless you >can state coherently and correctly what the definition is, then it >will cause you problems when you try to use it.