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the linux file system satisfies the zf axioms (lemmy.world)
submitted 1 year ago by to c/mathmemes@lemmy.blahaj.zone
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[–] 25 points 1 year ago (6 children)

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.

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  • [–] 8 points 1 year ago

    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.

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    • [–] 15 points 1 year ago (6 children)

    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!

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  • [–] 5 points 1 year ago (2 children)

    5 is bogus, too. You can’t create a folder by copying files into a[n already existing?] directory.

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  • [–] [S] 2 points 1 year ago (2 children)

    oh 8 is the axiom of infinity, 4 is the pair set axiom

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    • [–] 3 points 1 year ago

    "Math isn't useful"

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