*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.