2021.10.18 02:16 twofingerjump [Category theory] Basic Isomorphism Proof Checks
I would like proofs checks on two theorems
(1) Prove for any set A is isomorphic to itself
For there to be an isomorphism between sets X and Y we need functions
f: X -> Y and g: Y -> X
that satisfy the following compositions:
(g o f) = id_X
(f o g) = id_Y
we will check these compositions are satisfied.
let g=id_A: A -> A
we see that by substitution
(id_A o id_A) = id_A
let f=id_A: A -> A
and we see that by substitution
(id_A o id_A) = id_A
thus the compositions for a isomorphism between f:A->A are satisified and hence A is isomorphic to itself
(2) Prove for any sets A, B id A is isomorphic to B, then B is isomorphic to A
Assume A is isomorphic to B then there are functions
(g o f) = id_A
(f o g) = id_B
B is isomorphic to A if we have the compositions:
(f o g) = id_B
(g o f) = id_A
But due to A being isomorphic to B, we already have such compositions satisfied
Therefore B is isomorphic to A
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2021.10.18 02:16 zenetizunamikaze Usa essa aba de comentários pra fazer suas perguntas e questionamentos filosóficos resumidamente
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2021.10.18 02:16 FixerTed Ford sucks
2021.10.18 02:16 dirtyharrison Know your Enemy: Klaus Schwab, Great Reset author
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2021.10.18 02:16 Thebrianna24 He stopped me from my maid duties and made a mess on my face.
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2021.10.18 02:16 I_Fr0st birds arent real
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2021.10.18 02:16 ajejejebrazocrew I feel like two friends of mine enjoy having me as a third wheel
I (m24), this summer introduced two friends of mine (m 22), (f 25) and now they’re a couple. After they have sex they have taken the habit to come by my house to talk, which wouldn’t be a problem if it happened that often. Also when I’m with them and they want to be isolated they tend to push for me to stay with them. In the past year I have got a lot close to both of them and they have helped me with stuff I wouldn’t be able to deal alone, but I’m uncomfortable in these type of moments as I have a complicated relationship with dating people (not much experience so I easily get hurt as those are all new types of feelings for me) Also the guy tried to join the military but after months of training got rejected (for a serious problem of mental health in his family) and has come back a week ago (the same day that he left to join) but hasn’t reached out until today, which is strange, I get that he’s hurting but I could have probably helped. What do you think I should do/say?
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2021.10.18 02:16 TheBinarySon [SPOILERS] Leviathan questions
Playing ME3/LE for the first time (never played me3 before) and just finished going through Leviathan part. I know vaguely what happens at the end/what the choices are, but for now I have some questions based on the explanation of things given by the Leviathan:
1.) Why didn’t the leviathans just kill the synthetics themselves, or instruct the intelligence to do the same? Thus they could let organics learn from their mistakes and make machines that didn't cause war.
2.) If the crucible can kill all synthetic life, why doesn’t it just do that instead of harvesting organics for a billion years? Again, this would let the organics live and learn from their mistakes.
3.) Why doesn’t the Reaper Intelligence and/or the Leviathans take notice of exceptions, like the organic/synthetic symbiotes Javik mentions or the peace between Geth and Quarians?
4.) Why did they hide if they can kill reapers?
Any insight is appreciated!!!
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2021.10.18 02:16 TheGothDragon What kind of Dragonfly is this? Found in Virginia.
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2021.10.18 02:16 sakrunnaderro If u need any social account hacked hmu
2021.10.18 02:16 ffehrle PlayStation 2 and Original Xbox for sale
Selling a slim ps2 and original Xbox. Both have all of the cables, a controller, and games included are Ps1: Crash 3 warped Ps2: Sly cooper 1, 2 and 3 Ps2: Tony Hawk pro skater 3 Xbox: Tony Hawk underground 2 Asking $150 OBO. Must be able to meet in Delaware county.
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2021.10.18 02:16 Harper3441 Tips for architecture formation
Hey guys, i’m a 3rd year architecture student looking for some help. I have had some good success through my classes to this point, but i’m looking to really step up my work. I’ve always gone with some pretty basic shapes for my architecture, nothing too crazy. But i’m designing a building for SpaceX and i want to make some architecture that looks something like the work of Zaha Hadid. Problem is, it’s a bit difficult to find a form that works. I was curious if anyone here had some recommendations for form finding? I’ve done some experimenting in grasshopper but it’s difficult to learn that software. At my university we use Rhino for our 3d modeling software. If you have any tips, please lemme know!
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2021.10.18 02:16 IndicationFlimsy3946 I hope these all die
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2021.10.18 02:16 ghosts_inthe_snow Florals from Seattle [Cannonet QL17 / Kodak ultramax 400 / 40mm]
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2021.10.18 02:16 Dannig178 Victoria Justice
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2021.10.18 02:16 cheeseburgeraddict It started with a Mustang Alpha... how did I get here...
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2021.10.18 02:16 Wrong_Mortgage1581 Have 170k who should I get ?
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2021.10.18 02:16 catlvr860 lexapro with or without food?
ughhh I’ve been starting lexapro (5mg) on top of my other anti-depressant and I cut the pill in FOURTHS so i’m literally only taking like ~ 1.25mg. but i’ve been taking it w dinner. my problem is i’m on my period and have been feeling nauseous so i skipped dinner. I’m trying to drink a smoothie rn so i can take the lexapro as i’ve heard of you take it w/o food it can make you feel sick. have any of you taken it without food ??? i’m already feeling sick so i’m scared to risk it. i hate this phobia and my period
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2021.10.18 02:16 SpankAPlankton I saw these sports games at a library sale, and I was curious to see if anyone had actually played them. If you did, how were they?
2021.10.18 02:16 leonardcrast In the market for a new hotas
Hey guys, need some brutally honest advice, I've had two x55 rhino's and a x52pro they are all broken/acting up. Looking for the best alternative. Considering winwing, Thanks
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2021.10.18 02:16 Kerbaljack I received a spoiler early least year, but it still hasn’t come to fruition?
2021.10.18 02:16 Hagisman Mages be cray
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2021.10.18 02:16 Gothic_Jay guys my pomeranion is eating its own poop... what do i do
2021.10.18 02:16 CutAdmirable6593 Bo-Katan Kryze & Ahsoka from The Mandalorian , quite a dynamic duo!
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