What I mean is the set |R equipped with two operations + and *, with + defined in the usual way and with * defined in ALMOST the usual way but with the twist that for all a,b > 0, -a (aka 0-a) times -b equals -(ab). Jim Propp On Wednesday, August 24, 2016, Dan Asimov <dasimov@earthlink.net> wrote:
On Aug 24, 2016, at 3:56 PM, Mike Stay <metaweta@gmail.com <javascript:;>> wrote:
On Wed, Aug 24, 2016 at 4:22 PM, Eugene Salamin via math-fun <math-fun@mailman.xmission.com <javascript:;>> wrote:
Better yet, can anyone write about the usefulness of such a mathematical object?
Characteristic 2 fields satisfy -1 * -1 = -1 and have lots of applications, but I don't know how they're "bad".
Many papers on algebra require fields to have "characteristic not equal to 2" and never look back.
These results holding only for p != 2 have got me very curious about what happens for p=2.
So: What are some basic results in algebra where the cases characteristic 2 and unequal to 2 come out different?
Dan
On Aug 24, 2016 3:18 PM, James Propp <jamespropp@gmail.com <javascript:;>>
Has anyone written in an accessible vein about all the bad things that happen when you decree that minus times minus equals minus instead of plus?
I might do this in my September blog post but I'm hoping someone else has beaten me to it.
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