6 ms·

In modern math all numbers are built on set theory which has the empty set as it's foundation. Empty set is more like 0 than 1. Check mate Unitarians.

layer8 3y ago
The empty set is 1 set. Can’t have 0 without 1.
- fuzztester 3y ago
  The empty set is the set with nothing, i e. no thing. So it doesn't need 1. ;)
  - coldtea 3y ago
    You start from 1 empty set though. If you could start from 0 empty sets, you'd have a point.
    - fuzztester 3y ago
      >You start from 1 empty set though. Sez who, zigactly? If you are coldtea, I am coldertea. As in, I love my tea colder than you do yours. And starts who? Not me. Don't kid around, dude. I dik around. >If you could start from 0 empty sets, you'd have a point. What if the set of empty sets has no element? :)
      - coldtea 3y ago
        Was the first comment under the influence of drugs? In any case, for the second comment: even if the set of empty sets has no elements, it's still ONE set.
        fuzztester 3y ago
        >Was the first comment under the influence of drugs? No, it was not. Regarding this whole subthread in which I participated, I did it for some mutual logic-chopping fun. But if you thought there was a chance it was, you shouldn't have replied to the second comment, because I would have been equally under the influence of the drugs for the second, if I had been so for the first comment. (Don't reply to a druggie.) After all, they were both done in one atomic comment transaction.
    - fuzztester 3y ago
      If I start from 0 empty sets, how do I have A point?
  - layer8 3y ago
    Wouldn’t the set without nothing be more fundamental?
    - automatic6131 3y ago
      Does the set of sets that exclude themselves exclude itself?
      - Akronymus 3y ago
        No, because it isn't a set, but rather a class.
        OJFord 3y ago
        A concept created at least partially to resolve this paradox.
      - fuzztester 3y ago
        That's a well-known old paradox, or close. Good on you, cobber. (AU slang :)
        fuzztester 3y ago
        See Russells's paradox: https://en.m.wikipedia.org/wiki/Russell%27s_paradox https://en.m.wikipedia.org/wiki/Russell%27s_paradox
    - fuzztester 3y ago
      Brilliant. Go to the top of the class, er, set. Oops, forgot, sets have no order. List, then.
      - fuzztester 3y ago
        Ordered list, I mean.
  - phkahler 3y ago
    >> The empty set is the set with nothing So it is A set. In fact it's "the set" that makes it a rather special one.
eru 3y ago
No. Set theory is just one possible way you can build up numbers and mathematics. You can just as well build up numbers and the rest of mathematics from different foundations. They are all equivalent. Just like running your programs on ARM or on x86 or a toaster is all the same, thanks to emulators. (That's assuming you have an arbitrary amount of memory, and don't mind differences in runtime length.)
bobbylarrybobby 3y ago
Which is more foundational: the wheel or the axle? Sets aren't worth much if you can't take unions, which is where 1 comes from.

layer8 3y ago

The empty set is 1 set. Can’t have 0 without 1.

fuzztester 3y ago
The empty set is the set with nothing, i e. no thing. So it doesn't need 1. ;)
- coldtea 3y ago
  You start from 1 empty set though. If you could start from 0 empty sets, you'd have a point.
  - fuzztester 3y ago
    >You start from 1 empty set though. Sez who, zigactly? If you are coldtea, I am coldertea. As in, I love my tea colder than you do yours. And starts who? Not me. Don't kid around, dude. I dik around. >If you could start from 0 empty sets, you'd have a point. What if the set of empty sets has no element? :)
    - coldtea 3y ago
      Was the first comment under the influence of drugs? In any case, for the second comment: even if the set of empty sets has no elements, it's still ONE set.
      - fuzztester 3y ago
        >Was the first comment under the influence of drugs? No, it was not. Regarding this whole subthread in which I participated, I did it for some mutual logic-chopping fun. But if you thought there was a chance it was, you shouldn't have replied to the second comment, because I would have been equally under the influence of the drugs for the second, if I had been so for the first comment. (Don't reply to a druggie.) After all, they were both done in one atomic comment transaction.
  - fuzztester 3y ago
    If I start from 0 empty sets, how do I have A point?
- layer8 3y ago
  Wouldn’t the set without nothing be more fundamental?
  - automatic6131 3y ago
    Does the set of sets that exclude themselves exclude itself?
    - Akronymus 3y ago
      No, because it isn't a set, but rather a class.
      - OJFord 3y ago
        A concept created at least partially to resolve this paradox.
    - fuzztester 3y ago
      That's a well-known old paradox, or close. Good on you, cobber. (AU slang :)
      - fuzztester 3y ago
        See Russells's paradox: https://en.m.wikipedia.org/wiki/Russell%27s_paradox https://en.m.wikipedia.org/wiki/Russell%27s_paradox
  - fuzztester 3y ago
    Brilliant. Go to the top of the class, er, set. Oops, forgot, sets have no order. List, then.
    - fuzztester 3y ago
      Ordered list, I mean.
- phkahler 3y ago
  >> The empty set is the set with nothing So it is A set. In fact it's "the set" that makes it a rather special one.

eru 3y ago

No. Set theory is just one possible way you can build up numbers and mathematics. You can just as well build up numbers and the rest of mathematics from different foundations. They are all equivalent. Just like running your programs on ARM or on x86 or a toaster is all the same, thanks to emulators. (That's assuming you have an arbitrary amount of memory, and don't mind differences in runtime length.)

bobbylarrybobby 3y ago

Which is more foundational: the wheel or the axle? Sets aren't worth much if you can't take unions, which is where 1 comes from.