this post was submitted on 03 Aug 2025
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In means you can map every element bijectively to one from the complex field AND addition and multiplication can be performed in either field without leading to contractions, i.e. a+b=c <=> f(a)+f(b)=f(a+b)=f(c) and equivalent for multiplication. This is the part that the meme fails to consider, because nowhere is addition or multiplication for this novel field defined.
"i do not give a single fuck" implies an additive identity fuck, and "I don't give two fucks" implies a multiplicative identity fuck. That's a start at least!
I'll give this some attention when time permits because this does not make things clearer, lol.
I'll start with what a field is and a complex field 🤞
ELI5: it means that for every number there's a matching fuck and vice versa.
Not only for any number of fucks there is a corresponding complex number, but the basic operations (+, -, x, /) work in the same way for fucks and complex numbers
Overall, if two things are isomorphic you can consider them « the same »
Good luck!
Hmmm. But what if fucks aren't fungible?