On 12/3/2025 4:10 PM, Alan Grayson wrote:
On Wednesday, December 3, 2025 at 2:37:35 PM UTC-7 Brent Meeker wrote:
On 12/3/2025 3:00 AM, Alan Grayson wrote:
On Tuesday, December 2, 2025 at 3:51:45 PM UTC-7 Brent Meeker wrote:
On 12/2/2025 1:24 AM, Alan Grayson wrote:
On Monday, December 1, 2025 at 10:37:16 PM UTC-7 Russell
Standish wrote:
On Mon, Dec 01, 2025 at 08:07:14PM -0800, Alan Grayson
wrote:
>
>
> On Monday, December 1, 2025 at 3:46:40 PM UTC-7
Russell Standish wrote:
>
> On Sat, Nov 29, 2025 at 11:13:05PM -0800, Alan Grayson
wrote:
> >
> >
> > On Friday, November 28, 2025 at 3:26:03 PM UTC-7
Russell Standish wrote:
> >
> > Sorry - I can't make sense of your question.
> >
> >
> > The Axiom of Choice (AoC) asserts that given an
uncountable set of sets,
> each
> > one being
> > uncountable, there is a set composed of one element
of each set of the
> > uncountable set
> > of sets. The AoC doesn't tell us how such a set is
constructed, only that
> we
> > can assume it
> > exists. So, in chosing an origin for the coordinate
system for a plane
> say, we
> > have to apply
> > the AoC for a single uncountable set, the plane. But
there's no way to
> > construct it. Does
> > this make sense? AG
> >
>
> I don't see the axiom of choice has much bearing here.
To choose an
> origin, we simply need to choose one point from a
single uncountable
> set of points. We label finite sets of points all the
time - geometry
> would be impossible otherwise - consider triangles
with vertices
> labelled A,B and C.
>
>
> You write "we simply need to choose one point from a
single uncountable set
> points", but how exactly can we do that! That's the
issue, the construction of
> the coordinate system. In fact, there's no credible
procedure for doing that,
> so
> we need the AoC to assert that it can be done. IMO,
this is an esoteric issue.
> For example, we can't just assert we can use the
number ZERO to construct
> the real line, since with ZERO we have, in effect, a
coordinate system.AG
>
Rubbish - it is not controversial to pick a set of
points from a
finite set of uncountable sets. As I said, we've been
doing that since
building ziggurats on the Mesopotamian plain. AoC is only
controversial when it comes to uncountable sets of
uncountable sets.
*It's subtle, maybe too subtle for you to see its relevance.
You're imaginIng throwing*
*a dart at a flat piece of paper, but that falls far short
of a viable/construction /of a *
*coordinate system on a plane. You can imagine it being done
and that's the extent*
*of your proof. AG *
A coordinate system is anything that supplies a unique set of
numbers to label every point such that the numbers are
continuous. I think you have and exaggerated idea of what
needs to be constructed.
Brent
Presumably, you have a more rigorous approach, say for R^2, by
imagining a plane, or using a piece of flat paper, and throwing a
dart at it to define the origin. AG
You can choose any point and make it the origin, which just means
you give it the label (0,0). No physics can depend on the choice
of origin or the coordinate system.
Of course, but how can one find any point on a thing which is
ill-defined in the first place?
You don't /find /a point on a thing. The coordinate system and the
origin are in mathematics, not in reality. That's why they can be
arbitrary. You just postulate a coordinate system and say I'll call the
center of the Earth the origin and z-axis to be the line toward
Polaris. No one can say, "That's wrong." because it's arbitrary.
Brent
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