What you write seems correct but doesn't address the issue I raised; namely, that the metric tensor is defined on pairs of vectors in the vector space in the tangent plane of the spacetime manifold, and yields *different *real values for most different pairs. So, it seems that the metric tensor FIELD is* NOT well defined*. AG
On Wednesday, September 4, 2024 at 6:02:17 AM UTC-6 John Clark wrote: > On Tue, Sep 3, 2024 at 6:44 PM Alan Grayson <[email protected]> wrote: > > * > I fail to see how your comments relate to the possibly ambiguous >> concept of the latter. The metric tensor field seems ambiguously defined.* > > > *A N dimensional space is composed of an uncountable number of real > numbers but it can be unambiguously defined by just N countable rational > numbers, you can pair them up one to one. This is possible because there is > only a countably infinite number of COMPUTABLE real numbers, the same rank > of infinity as the rational numbers. So you can in effect give a rational > number name to every real number you are able to find on the number line. > You can do this even for a number such as π which is not only irrational, > it's transcendental, because it is also computable. You can use an infinite > series to get arbitrarily close to π. * > > *The vast majority of numbers on the number line are NOT computable (and > have no name) but that's not really a problem despite the fact that the > vast majority of numbers on the number line are NOT computable because, > except for Chaitin's Omega Number, every number that a mathematician has > ever heard of is a computable number. Computable numbers can have names, > uncomputable numbers can not.* > John K Clark See what's on my new list at Extropolis > <https://groups.google.com/g/extropolis> > > und > > > -- 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 on the web visit https://groups.google.com/d/msgid/everything-list/4d3a324a-7212-43a7-9c7b-665fe897168en%40googlegroups.com.
