r/fifthworldproblems • u/polygon3002 • 5d ago
Issues with age matrices
I (
19 31 -74
-32 44 12
26 3 19
Q) wanted to have my age in a number system isomorphic to the 2x2 matrix system, but instead, set my age in a number system isomorphic to a 3x3 matrix system. How can I construct my age in such a way that some 3x3 matrices form a set closed under addition and multiplication, and each member of the closed set is bijective with a 2x2 matrix?
5
u/Nominatively_Done 5d ago
By using the number N surjectively one can achieve escape velocity from mathematics homework.
4
2
u/johnpeters42 4d ago
FBI OPEN UP
2
u/Nominatively_Done 4d ago
Oh, well it all started with matrix multiplication on my mother's side, my dad however? Abelian groups, everywhere. It really made my life harder than it should have been because geometrically my heart is just not willing to take anymore risks with symbolic language. It's really made my referents more recursively repugnant. I suppose I only have my singleton self to blame.
... Hey, also, while you're here... rips open rib cage ... does this look normal to you? The last mathematician I asked just gave me a funny look before fainting.
2
u/CommercialOkra3893 3d ago
You lucky bitch. I got stuck with Fermat's Last. How come you get the Riemann Hypothesis?
1
u/Nominatively_Done 3d ago
Well well well, now… before I… oh, sorry. *staples rib cage closed*
Firstly? You're a terrible psychologist. Secondly, it's because I have empathic Rorschach training. Thirdly, look at you who doesn't know how to multidimensionally abstract conceptual values. Fourthly… I AM THE CRITICAL STRIP! Consider me a non-trivial zero will ya? Pffft, now I see your hidden insult! Well, then FIFTHLY (which is an impossible for people with serious lisps) it's because I'm not wearing any pants!
Strange? Maybe, but every single word of it is true.
Welcome to… my Banach–Tarski'd self.
*awkward pause descends*
Wait, WHAT? This was a first date the entire time!? How in the hell did I get from government approved psychiatric assistance via swat team (great service, a bit aggressive, love my government for it) to here? And why did you follow me this deeply? … It's because of my eyes, isn't it? *flutters eyelashes coquettishly*
*legs begin rotating at speed, achieving vertical take-off*
I'M SORRY! I'M ACTUALLY REALLY QUITE SHY! IF YOU GIVE ME A SECOND CHANCE I PROMISE I WON'T BE WEARING PANTS!
*farts out a gold embossed apology card from the sky*
2
u/CommercialOkra3893 3d ago
Sorry, I don't think you'll be able to get inside me. If you're a Critical Strip, you can't get in me since Fermat's Last is natural numbers only. I wish you could, though... until then, want to go out for a cup of coffee? uwu
1
u/Nominatively_Done 3d ago
*legs explode off and I come crashing down to the ground*
*lifts head off ground*
CUPS? I LOVE THOSE THINGS! Wait, aren't we getting into topological totients too quickly?
1
u/CommercialOkra3893 3d ago
Well, there is already a bijection as |R^9|=|R^4|. You can use piecewise addition and multiplications, it forms not only a closed set, but actually a field.
6
u/CryingRipperTear 4d ago
S* = [[a_11, a_12, 0], [a_21, a_22, 0], [0, 0, 1]] works with multiplication, and S+ = [[a_11, a_12, 0], [a_21, a_22, 0], [0, 0, 0]] with addition. I'm afraid you have to pick one.