Re: Michael Wood documentary proves Oral Traditions are a lie

Am Thu, 6 Sep 2007 11:38:36 -0400 schrieb Brian M. Scott:

On Thu, 6 Sep 2007 07:43:54 +0200, Joachim Pense
<snob@xxxxxxxxxxxxxx> wrote in
<news:jyitzt1093nk.1qomjz1ahj47h.dlg@xxxxxxxxxx> in
sci.lang:

Am Wed, 5 Sep 2007 14:07:16 -0400 schrieb Brian M. Scott:

On Wed, 5 Sep 2007 18:34:41 +0200, Joachim Pense
<snob@xxxxxxxxxxxxxx> wrote in soc.history.ancient,sci.lang:

Am Tue, 4 Sep 2007 11:09:22 -0400 schrieb Brian M. Scott:

[...]

Even in the extended reals (including infinity and
-infinity), defining x/0 is problematic: the statement
that x/0 = y should mean that 0*y = x,

why?

Because that's essentially the definition of division in any
field. Given a field F and x, y in F with y != 0, we define
x/y to be x * y^(-1), where y^(-1) is the unique element of
F satisfying y * y^(-1) = 1_F. It follows at once that if
x/y = z, then z = x/y = x * y^(-1), and hence z * y =
x * y^(-1) * y = x * 1_F = x.

sure, but when you extend the field of the reals by two
elements and try to extend the operations to the
extension in a meaningful way, you cannot expect to keep
all properties of these operations.

I can expect to keep definitional properties. If that's
impossible, then I prefer to give the operation a different
name.


Oh, then you should rename the operations of infinite ordinal
arithmetics.

Joachim
.