Responding mostly to mjsd:
Pseudovectors are also sometimes called bivectors in the 3d case (in case someone is googling for further information). The main difference between wedge and cross is that wedge products produce multicomponent objects (essentially antisymmetric tensors). It is...
I have at home a book called 'A Modern View of Geometry' (can't recall the author's name just now) in which the properties of projective spaces are gradually developed through a series of finite point models of the axioms. Hand in hand with this, the author sets up an algebraic structure, which...
@Hurkyl
Got it! Thanks. I must be having a bad day, because it's obvious now that you mention it. Of course, the axioms are the same as for standard analysis when the new predicate "standard" is not used, so of course all the usual results follow whenever no distinction between standard and...
Thanks! I had forgotten this (or never new, perhaps), as I have been more interested in the surreals than the hyperreals lately.
No special reason why, I just mentioned larger ordinals as an example of a possible extension. BTW, could you give me a reference on the hypernaturals indexing the...
While I fully agree with the correct subset of the arguments given above (you know who you are), it seems to me that there is a genuine ambiguity in the notation 0.999.... Caveat: Of course the real number system is defined axiomatically, so questions about the notation resolve ultimately not...