The first thing people ask (I think) is “What is i?” But this question actually has many shades of meaning. It takes on extra piquancy after one realizes that the definition of i as the square root of -1 doesn’t distinguish i from -i, and that this ambiguity undermines the use of the word “the” in the definition. So I think one natural sequence of questions is “What is i?” “Okay, but what is i, really?” “How can we tell i from -i?” “How do I know that my i isn’t your -i?” “Wait a minute, so what is i again?” Jim Propp On Tue, May 19, 2020 at 8:55 AM Veit Elser <ve10@cornell.edu> wrote:
On May 16, 2020, at 1:54 PM, Keith F. Lynch <kfl@KeithLynch.net> wrote:
The *second* thing everyone asks when they learn about i is which number is i and which is -i. Imagine the horror if they go through their whole mathematical career getting those two swapped.
I’m curious, what’s the *first* thing?
It’s actually very cool that the Galois automorphism i <-> -i is co-opted by physics in the time-reversal transformation. The real numbers turned out to be incomplete in a very real sense!
-Veit _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun