Originally posted by Soothfast
A group is necessarily associative, so that is why DeepThought doesn't give that the set is a group.
Yes, I noticed that. Perhaps I'm being too picky, yet I would have liked
DeepThought to have spent more time setting up the problem like this:
Let S be a set (of what?). Let an operation K be defined upon the elements
of S such that ... results in a product X. Then (state the problem).
That's how I liked to write problems and how I prefer problems be written.
I find it harder to comprehend--without making too many asssumptions--
what's meant by mathematical problems presented in a popularized way.
Whenever I hear a non-mathematician speak of 'the group of people in
this room', then I don't assume that all the group axioms must hold here!
I suppose that I believe the challenge in a problem should be in tackling
the concepts involved rather than in struggling to figure out the problem's
needlessly obscure, sloppy, or confusing terms. Or perhaps, as I grow
older, I have increasingly less patience with wasting my time deciphering
what a problem means when the writer easily could have made it clearer.
Yet I know that DeepThought did not quite understand some of my recent
recreational mathematical problems, so he asked me to explain what I
meant, and I did so to his satisfaction. I thought that much of what he
wrote in his attempts to solve these problems was too confusing for me
to follow easily (without doing more work than I would like in a hurry), so
I skipped to the parts that I could quickly check. I suppose that I generally
have some difficulties with DeepThought's style of mathematical exposition.