On Tuesday, September 17, 2024 at 11:16:10 PM UTC-6 Alan Grayson wrote:
On Tuesday, September 17, 2024 at 7:49:17 AM UTC-6 Alan Grayson wrote: On Tuesday, September 17, 2024 at 6:48:19 AM UTC-6 Alan Grayson wrote: 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 * *Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2? So your plot seems wrong, but it's what is on the Internet. AG * *That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I still think the plot keeps repeating as x increases or decreases. AG* *It repeats as follows: Arctan(x) = Arctan(x + n*2*pi), n=0,1,2,3 ... AG* [image: image.png] -- 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/04003ae7-8fe2-43ed-b564-7a70a160d499n%40googlegroups.com.
