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Okay, so:

🍇 = 1, because 1 + 1 + 1 = 3
Therefore, 🍪 = 2, because 2 - 1 - 1 = 0
🥪 is the set of all integer numbers Z, as defined
I am not sure about 🍔, but I assume that it’s the set of integers with all even numbers removed, therefore it’s the set of all odd numbers.

Beyond that starts the nonsense for me. I’m very curious whether that stuff actually checks out. Some of the terms I remember from group theory, but other stuff seems incorrect to my (limited) knowledge.

The second definition of 🍕 seems to contain redundant information, as afar as I can see " --> " defines a morphism, so why is the predicate “φ is a morphism” matter?
The first definition of 🍕 with the contravariant thing also doesn’t parse for me, what does that “-” mean in the function arguments?
In the definition of 🌭, what is the n (or the P)? ChatGPT started yapping about real projective space, but I’m not sure if that’s correct.

If there’s an actual mathematician here who knows then I’d love to know the answer. I’ve kinda been nerd sniped by this question but I don’t possess the knowledge to fully get this one

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kogasa@programming.dev ⁨7⁩ ⁨hours⁩ ago
🍕(–, B) : C -> Set denotes the contravariant hom functor, normally written Hom(–, B).

In this case, C is a category, and B is a fixed object in that category. For any given object X in C, the hom-set Hom(X, C) is the set of morphisms X -> B in C. For a morphism f : X -> Y in C, the Set morphism Hom(f, B) : Hom(Y, B) -> Hom(X, B) is defined by sending each g : Y -> B to gf : X -> B. This is the mapping C -> Set defined by Hom(–, C), and it’s a (contravariant) functor because it respects composition: if h : X -> Y and f : Y -> Z then fh : X -> Z and Hom(fh, C) = Hom(h, C)Hom(f, C) sends g : Z -> B to gfh.

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- gerryflap@feddit.nl ⁨4⁩ ⁨hours⁩ ago
  Okay I have some reading to do haha. Thanks for the explanation!
  
  As a programmer (who also did quite some math) it never ceases to amaze me how often math just uses single character variable/function names that apparently have a specific meaning. For instance the P^(n)® thingy. Without knowing this specific notation, one might easily assume it meant something else like power sets. Even within the niche I’m more familiar with (machine learning) there was plenty of that stuff going around.
  
  Then again, this meme has an incentive to make it harder, it wouldn’t be funny if it explained symbols.
  
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  - kogasa@programming.dev ⁨4⁩ ⁨hours⁩ ago
    Math builds up so much context that it’s hard to avoid the use of shorthand and reused names for things. Every math book and paper will start with definitions. So it’s not really on you for not recognizing it here
    
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MBM@lemmings.world ⁨12⁩ ⁨hours⁩ ago
🍔 is the set of integers modulo 2 (more literally, if two integers differ by an even integer you consider them the same). I can write out the rest in a bit.

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- gerryflap@feddit.nl ⁨4⁩ ⁨hours⁩ ago
  Ah thanks for the info! Together with the other in-depth comment this is painting a good picture of what’s happening. Though I have some terms to study before I’ll get it.
  
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Zenoctate@lemmy.world ⁨14⁩ ⁨hours⁩ ago
All I can say is that P(ℝ) refers to a power set of ℝ (all rational numbers). Although I don’t know what n stands for in Pⁿ(ℝ)

Basically P(A), where A = {1,2,3}, equal {Φ,1,2,3,(1,2),(2,3),(1,3),(1,2,3)}

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- gerryflap@feddit.nl ⁨13⁩ ⁨hours⁩ ago
  Yeah this was a possibility I was thinking as well. The superscript n could just be n recursive applications, but then n is still not defined. It’s one of the things that makes me thing that it’s just nonsense. Also, how do you do math on Lemmy? Can you just use LaTeX math syntax or did you copy those symbols?
  
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  - kogasa@programming.dev ⁨7⁩ ⁨hours⁩ ago
    It’s real projective space
    
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  - Zenoctate@lemmy.world ⁨12⁩ ⁨hours⁩ ago
    Wrote it from my phone using Unexpected Keyboard app with Greek symbols included and used superscripts and subscripts feature. I just used the markdown feature of writing code to create some formatting. Like this A = {}
    
    Also this post is nonsense, hence posted here.
    
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    kogasa@programming.dev ⁨7⁩ ⁨hours⁩ ago
    It’s not nonsense, although there is a typo that makes it technically unsolvable. If you fix the typo, it’s an example calculation in the wikipedia page on cohomology rings.
    
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