Of course. How does this help? AG On Wednesday, September 4, 2024 at 12:43:02 PM UTC-6 Brent Meeker wrote:
> Most different vectors are different lengths. > > Brent > > > > On 9/4/2024 5:08 AM, Alan Grayson wrote: > > 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 > > <https://groups.google.com/d/msgid/everything-list/4d3a324a-7212-43a7-9c7b-665fe897168en%40googlegroups.com?utm_medium=email&utm_source=footer> > . > > > -- 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/5182bee9-32ed-42e2-8a1d-07a1d5250f13n%40googlegroups.com.
