Re: [math-fun] Dimension of real division algebras

You mean to say: Finite dimensional real division algebras. There are lots of infinite dimensional real division algebras. Some examples are the fields of rational functions R(x), R(x,y), etc.

Thanks for pointing that out -- it hadn't occurred to me. (Plus, I seem to recall JHC's stating in this venue that there exist no infinite-dimensional real division algebras.)

But I see no problem with R(x), etc., as real division algebras.

I would guess he meant no infinite dimensional real division algebras that are not fields. I may as well join the club and state a favourite theorem: A polynomial of degree n with coefficients in a field K has at most n roots in K. Elementary to prove and yet has a lot of consequences. Gary McGuire