It's nice to see people not only responding to my posts, but saying really interesting and informative stuff as well. Shame I can't think of a way to make it on topic.... In a message dated 1/27/2003 4:29:41 PM Eastern Standard Time, Michael Barr <barr at barrs.org> writes: > Ok, here is one in math. The proof of the chain rule in > nearly all calculus books is wrong. The funny thing is > that a correct proof is not especially harder than the > incorrect proof. Hmm.. I can't seem to pull up a memory of that proof; could you post both versions? > There are cases where we tell lies because the truth is too > complicated. Here's one: it is assumed that you can add > and multiply infinite decimals and the truth is that you > can, but the rules are so complicated that they are hard to > describe. Think, for example, how to double > .555555555555.... (unless you say that 5/9 + 5/9 = 10/9 = > 1.111111111...., in which case I will give you a number in > which 5s and 6s appear at random). Most of the lies would > be too complicated to describe here. I don't remember any math class asking us to manipulate unending decimals. We were shown that some fractions produced such things, but never took it further. If I had to manipulate them, I'd just convert them to fractions (which is likely where they came from in the first place) and deal with them that way. --KG