> > Dear Heinz, > > Well I think I will leave it up to you to parse the distinctions between > "not founded" and "invalid", In any case these foundation issues are > something you brought up and, in my view, irrelevant. One thing is > clear, though you seem unwilling to admit it, Dedekind was wrong to say > that the then accepted understanding of number as a ratio could not be > extended to include complex numbers. Whether a better way is a matter > of taste, not history. > Dear Bob,
As long as you do not see the difference between "not founded" and "invalid", you will not have understood Dedekind's remark your are critizising. "Foundation" is Dedekind's point, not mine.
I do not see how Euclid's book V can be extended to include also the complex numbers in its theory of proportions. What you are saying in your postings is to vague for me as a mathematician to point to the place where the reals come in. I am sure they come in at a crucial point whilest constructing the complex numbers.