Hi Corey,

It's "Dedekind". He was a German mathematician:
Julius Wilhelm Richard Dedekind.

If you search on "Dedekind cut" you'll find lots of references.
In short, Dedekind cuts are a way of defining the real numbers
in terms of the rational numbers.
Dedekind cuts do it via subsets of the rationals that are
defined using the standard ordering.
"Dedekind cut arithmetic" is probably a way of defining the
arithmetic operations on the reals in terms of operations on
subsets of the rationals.

Another popular way to define the real numbers in terms of the
rational numbers is via equivalence classes of Cauchy sequences.
If you search on "Cauchy completion" you'll find out more.
Incidentally, Cauchy was a French mathematician:
Augustin Louis Cauchy.

Walter

--- Corey Bray wrote:
> Hello group,
>
> I'm trying to learn about something called, and please correct my
> spelling, "Dedican Cut arithmetic". Does anyone know what it is? I'm
> reading a book on Advanced Calculus, well I am actually listening to it
> on tape, but that has caused me some difficulty here. If anyone can
> explain what this type of arithmetic is and how it works, I would really
> appreciate it.
>
> Corey...