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. 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/aS4aw9M8RzxKaOfa%40zen.
