ThePanda

Must do work, so much to do, however do not wish to work, inclined to do so many other things which are not work, and yet bored from a lack of things to do.

Do not read the rest of this unless you wish to see me stumble around relatively simple aesthetic details. BTW, I love the fact that all the new browsers spell check, I would never have been able to spell aesthetic otherwise.

In other news, has anyone noticed the annoyance with trying to figure out what infinite generalizations of vector spaces over finite fields are? I have been working on this proof which works well on vector spaces over finite fields, and on vector spaces over countably infinite fields, and while the rationals are a perfectly good countably infinite field, the integers, which are oh so much simpler to write out, aren’t, at least not with the natural definitions of multiplication. I don’t really care that much about multiplicative inverses, and such, but it would just be cleaner to write out if I could sort of assume a different multiplicative operation on the natural numbers, probably one implied by passing multiplication between rationals through whatever bijection you use between naturals and rationals. More precisely (bear with me, no tex here, and hence I am just going to post tex code).

Given $f:\mathbb{Q} \rightarrow\mathbb{Z},
f(a*b) = f(a) *’ f(b) for some operator * and *’

This is all a moot point really, it would just make some of this cleaner, and quite possibly this is all a result of missing an obvious way to do this cleanly, for instance talking about points in a vector field over a countably infinite field F, and using the L_2 norm as I should have been all along, rather than complaining about this. Oh well, now to convince myself to work. Anyone noticed how narrowing a problem for yourself, to specifically make a proof easier is hard, it either ends up being too narrow, or too hard. Bah, I need to take more math next semester, its been too long since I stepped into a math class.

Ze Panda