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 Indeed not only would geometry be impossible if we couldn't do this, so would engineering. ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders [email protected] http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/386f1c2f-928c-4f10-88a6-dc7983f31fbdn%40googlegroups.com.
