On Tuesday, September 17, 2024 at 4:57:12 AM UTC-6 John Clark wrote:
On Mon, Sep 16, 2024 at 11:46 PM Alan Grayson <[email protected]> wrote: > How would you map (0,1) 1-1 onto the real numbers? *F(x)=1/2 + 1/π Arctan(x) . The domain is all the real numbers and the range is (0.1)* *> This map isn't 1-1. Many x's correspond to the same point in (0,1). AG * *This is a graph of the Arctan function. Show me many X's, or even one X, that corresponds to the same point in y.* *I'll get back to you on this. I was thinking, as x increases positively or negatively, the y values (angles) repeat multiple times, making the function many-to-one. In this case, we're mapping all the real numbers, to a subset of the y-axis. Am I mistaken? AG * [image: image.png] *>> If a set is infinitely large then there is a proper subset of that set that can be put into a one to one correspondence with the entire set, in fact that is the mathematical definition of "infinity".* *> That's circular. AG * *>I deleted the post with the circular comment. Why are you responding to it? AG* *I responded to your email. Apparently you thought you knew a way to delete an email that was already on my computer or delete my memory of reading that email. Neither worked. * *I deleted it from the List, wherever it's located. AG * *> an infinite universe cannot be created. If one exists, it is eternal. The reason is because the creation would require something non-physical; infinite spatial expansion instantaneously. So no BB for a spatially infinite universe.* *I will now quote somebody named Alan Grayson "You keep doing the same thing; asserting a result without proving it " * *Actually, I did prove it, above. When a universe is created, or shall we say "comes into being" it can either be finite or infinite. If it's alleged to be infinite but doesn't include some spatial points, that would be a contradiction to the assumption that it's infinite, and thus it must be finite (since, as we agree, a universe cannot transform from finite to infinite, or vis-versa). OTOH, if it's really infinite and includes all of space, it couldn't have reached that state through any progressive evolution, as that would make it finite. So, if the universe is really infinite, it must be eternally infinite since it can't evolve to that state. Not every proof is mathematical. This one's based solely on logic. AG* -- 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/a53700bd-121c-4542-988f-e90a67d00c2dn%40googlegroups.com.
