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.
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.
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!
15 Comments
november@piefed.blahaj.zone · 25 pts · 292d
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.
whimsy@lemmy.zip · 13 pts · 292d
Yep, they'd have different inodes. But one could argue about the definition of equality...
Nonetheless, a very interesting post!
pixeltree@lemmy.blahaj.zone · 2 pts · 292d
Java coming in with the == vs .equals()
lemmyng@piefed.ca · 11 pts · 292d
The two folders'
.would be different.falcunculus@jlai.lu · 7 pts · 292d
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, butnew 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.
lastunusedusername2@sh.itjust.works · 5 pts · 292d
But is it the "same" file or just an identical one?
Slotos@feddit.nl · 2 pts · 292d
If you tar the contents of the two, you’d be unable to attribute the archives to any specific one.
ns1@feddit.uk · 15 pts · 292d
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!
bleistift2@sopuli.xyz · 5 pts · 292d
5 is bogus, too. You can’t create a folder by copying files into a[n already existing?] directory.
siriusmart@lemmy.world · 2 pts · 290d
i was trying to say this command
would create the union folder
bleistift2@sopuli.xyz · 1 pts · 289d
Oh. Your original 5th axiom didn’t mention unions.
siriusmart@lemmy.world · 2 pts · 290d
oh 8 is the axiom of infinity, 4 is the pair set axiom
ns1@feddit.uk · 1 pts · 288d
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.
siriusmart@lemmy.world · 2 pts · 286d
yeah its OC
somerandomperson@lemmy.dbzer0.com · 3 pts · 292d
"Math isn't useful"