On Wednesday, September 18, 2024 at 7:34:58 AM UTC-6 Alan Grayson wrote:
On Wednesday, September 18, 2024 at 6:33:35 AM UTC-6 Alan Grayson wrote: On Wednesday, September 18, 2024 at 6:20:04 AM UTC-6 John Clark wrote: On Wed, Sep 18, 2024 at 8:12 AM Alan Grayson <[email protected]> wrote: On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote: On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson <[email protected]> wrote: *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* [image: image.png] *1) **The range of the Arctangent function is the interval (-π/2,π/2) and its range is all the real numbers.* *2) By dividing by π, the range scales to (-1/2, 1/2).* *3) Adding 1/2 shifts the range to (0,1) * *4) Thus for every real number x there is a unique number y between zero and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) . As I said before, the domain is all the real numbers and the range is (0,1)* *> Yes, but initially you were seeking a 1-1 function, but this one is many-to-one. AG * FOR DARWIN'S SAKE! I GIVE UP! *Y**ou ought to cease being a juvenile a'hole. At each x, we get a value of y, but this image repeats as x is incremented by 2pi. Same situation at every x in the domain. Thus, many-to-one. But what really interests me is my claim/proof that an infinite universe must be eternal and hence is not subject to a creation. AG* *I could be mistaken about arctan function. I'll check this again. AG* *I admit it's puzzling. Whereas tangent 0 degrees = tangent 360 degrees = 0, and arctan 0 degrees = 0, arctan 360 degrees ne 0. This is how I concluded y = arctan(x) is many-to-one. 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/902c629b-61f5-4da4-b665-4606253d9c44n%40googlegroups.com.
