On Tue, Sep 3, 2024 at 10:07 AM Alan Grayson <[email protected]> wrote:
*> While spacetime might not have an infinite set of events, countable or > uncountable, the tangent space is constructed via a vector space with at > least a countable number of elements. * Even though there are an uncountably infinite number of real numbers but only a countable number of rational numbers, you can always find a rational number that is arbitrarily close to any real number, provided that the real number in question is computable. Thus the thing that you're so worried about is not a concern for a physicist because, at least so far as anybody knows, there is no physical experiment you can perform that can reveal the difference between the countable infinite and the uncountable infinite. Mathematics is the language of physics but mathematics is not physics. And any language can be used for both fiction and nonfiction, so it could be that the hierarchies of infinity and even the very concept of infinity is the mathematical equivalent of a Harry Potter novel. Mathematical consistency may not be enough to ensure physical reality. John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis> acr > -- 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/CAJPayv0qcsG4eYQiT_QyFRbipkHJTxncOBqXWHGhNXso%3D%2B11EQ%40mail.gmail.com.
