I'm a Software Developer by profession, not a Mathematician, or Physicist, so please be patient with my ignorance as I'm about to ask (what I am sure is) a very basic question about Clifford Algebra. I've been reading some Clifford Algebra books I have, on how C.A. represents and performs math on Vectors. Aside from the aspect of k-blades to represent dimensions in C.A., I have not yet found ANY difference at all, between "standard" Vector Math that can be found in any basic book about Vectors, and how Clifford Algebra performs mathematical operations on Vectors! I see inner and outer products being used in any book I pick up and read some pages about math with Vectors. I also see all of the standard mathematical operations on Vectors being the same as I've read so far, in the Clifford Algebra book's Chapter on Vector Math. The only thing I don't recall seeing in standard math books about Vectors, that I do see in Clifford Algebra is the addition of the inner and outer products to form a geometrical product. Is the geometrical product, and the use of k-blades, about the only difference I should expect to find, when comparing C.A.'s treatment of Vectors, with how Vectors are operated on in standard Algebra's treatment of Vectors??? I'm REALLY confused why I'm not seeing any huge difference yet. Can you shed any light on this, and should I expect essentially no differnce between Clifford Algebra's treatment of Calculus, and what can be found in any standard Calculus book (aside from some differences in symbols used??? Admittedly, I am not yet done with my reading the section of the Clifford Algebra book having to do with Vectors, but I have not yet seen ANY differences in mathematical operations, including many of the symbols used.