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Do the mathematical inverse and identity elements exist for convolution?

Started by Charles Krug April 23, 2005
On Thu, 28 Apr 2005 17:03:31 -0700, Jon Harris
<jon_harrisTIGER@hotmail.com> wrote:
> "Jerry Avins" <jya@ieee.org> wrote in message > news:c-udnb5AJYDC9uzfRVn-ow@rcn.net... >> Jon Harris wrote: >> >> ... >> >> > My assumption was that for many text books, the class-assigned >> > market is the vast majority of sales (though I'm sure there are >> > exceptions). >> >> There doesn't seem to be much price competition for that market. Do you >> suppose that kickbacks are somehow involved? > > I really don't know anything about the textbook racket, but I would > guess it's an issue of spending someone else's money. I've heard that > it is very common that, when specifying something that you don't have > to spend your _own_ money on, there is much less incentive to save > money. The profs don't really care how much the students have to > spend (within a fairly wide window of "reasonable"), so there isn't > much incentive to specifying cheaper books. Besides, for most US > colleges, the books are a small expense compared with tuition, > room/board, etc.. >
Have you read Richard Feynman's experiences serving on the California textbook committee? It's in "Surely You're Joking, Dr. Feynman" but also online here: http://www.textbookleague.org/103feyn.htm
On 28 Apr 2005 22:51:36 -0700, Rune Allnor <allnor@tele.ntnu.no> wrote:
> > James Van Buskirk wrote: >> "Charles Krug" <cdkrug@worldnet.att.net> wrote in message >> news:ig6be.643620$w62.333967@bgtnsc05-news.ops.worldnet.att.net... >> >> > I'm borrowing Matlab's term in this case. >> >> > I'll have to think about James' "countably long" case. You can't >> > easily convolve ( . . ., 0, 1, 0, . . , ) given finite memory, > which I >> > suppose points out the difference between math and implementation. >> >> Permit me to point out that in your first post to this thread, >> you said: >> >> > Mathworld is helpful in showing that it's commutative, associative, > and >> > distributive, so if it's a group, it's also abelian and a field > with >> > addition. >> >> The closure under addition is inconsistent with the properties >> of Matlab vectors: try adding [1 0] to [1 0 0]. That is one >> reason that I viewed the elements of the vector space in question >> as I did. > > That's because the vectors belong in two different vector spaces. > A vector space is defined by its "underlying field", i.e. whether > the coefficients are real or complex numbers, and the dimension. > Continuous vector spaces are of infinite dimension, but in these > cases the range [a,b] must be specified, > > f(x), a <= x <= b > > Rune
My fault as the OP for being imprecise with my use of "vector," I'm afraid. I Should have reserved it to mean "ordered n-tuple of numbers" rather than munging it up with the programming definition.
Charles Krug wrote:

   ...

> Have you read Richard Feynman's experiences serving on the California > textbook committee? It's in "Surely You're Joking, Dr. Feynman" but > also online here: > > http://www.textbookleague.org/103feyn.htm
I did, long ago. I remember the drift (which I know from other sources; it hasn't changed much except in biology, where it's gotten worse). The only part of the details I remember is that it concerned K...12. Jerry -- Engineering is the art of making what you want from things you can get. &#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
Charles Krug wrote:

> Have you read Richard Feynman's experiences serving on the California > textbook committee? It's in "Surely You're Joking, Dr. Feynman" but > also online here: > > http://www.textbookleague.org/103feyn.htm
Fabulous! Ciao, Peter K.