5 ms·

To be pedantic, `f(x) = 0` is a function of x.

• dahart 10mo ago
  Yeah, true. Is there a proper math term for a function of x that does not depend on x?
  • MarkusQ 10mo ago
    That's called a constant.
    • dahart 10mo ago
      That’s not quite the word I was looking for, since a function returning a random number isn’t a constant, and also doesn’t depend on it’s inputs.
      • MarkusQ 9mo ago
        If we're talking "proper math terms", if it "returns a random number" it isn't a function. In math, the value of a function can't change unless the arguments change. If you evaluate it repeatedly with the same argument(s) you'll always get the same result.
        • dahart 9mo ago
          Yes, you’re right, good point. Maybe there is no one good term for this case (but given the ocean of terminology, I’d be slightly surprised). ‘Not a function’ also isn’t the right term here because functions of x that returns a constant are okay - they just don’t depend on x. Hashed random functions are true functions but are designed to be non-invertible, so maybe non-invertible (or irreversible) is a decent single term for what @vunderba meant. Other terms that broach it might be ‘non-injective’ and ‘entropy-reducing transform’. I suspect those aren’t technically strong enough for the kind of information loss we need in this context.