Not sure about number 2. You can have two folders that have identical contents but aren't the same folder. I don't think anyone would reasonably use the word "equal" to describe that situation.
this post was submitted on 15 Nov 2025
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Yep, they'd have different inodes. But one could argue about the definition of equality...
Nonetheless, a very interesting post!
Java coming in with the == vs .equals()
The two folders' . would be different.
In computer science this difference is called value types vs identity types. Value types are "equal" if their value is the same whereas, identity types are "equal" if they are the same actual instance. So what "equal" means changes.
For instance (using fantasy syntax), new Vector(1,2) == new Vector(1,2) as they are conceptually the same object, but new Person ("John Smith") ≠ new Person ("John Smith") as two persons can be different people even of they share their name, so they cannot be assumed to be the same.
I have no idea how this maps to actual math though.
But is it the "same" file or just an identical one?
If you tar the contents of the two, you’d be unable to attribute the archives to any specific one.
The one that's most obviously wrong is no. 4, which I think is meant to be the axiom of infinity, as this would imply every filesystem has a folder with an unlimited number of files. Probably several others have issues as well.
But maybe you can get around it if you imagine an idealised infinite linux filesystem rather than an actual real example!
oh 8 is the axiom of infinity, 4 is the pair set axiom
Ah that makes sense thanks. It's cool how symlinks can give a kind of infinity.
Is this OC? I didn't realise at first, it's a fun idea well researched.
5 is bogus, too. You can’t create a folder by copying files into a[n already existing?] directory.
i was trying to say this command
mkdir union
cp -rf A/* union
cp -rf B/* union
would create the union folder
Oh. Your original 5th axiom didn’t mention unions.
"Math isn't useful"