4 ms·

Null is closer to ‘empty set’ than to zero, and the two concepts are similar but different enough to be distinct.

dayjaby 2y ago
In German, it's the same. I hope you are not talking about null in coding? Because I'm pretty sure human 2000 years ago did not know any programming code or even empty sets.
- deleted 2y ago
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- rdtsc 2y ago
  Empty set idea doesn’t seem so abstract. A bag of stuff can have nothing in it, so it’s empty. Combining and splitting up containers of items would have been an everyday occurrence.
kreetx 2y ago
I'm just nitpicking, but it's unlikely that the inventors of both had empty set and zero formalized to a degree to make them distinct.
- adrian_b 2y ago
  While the empty set and the number "zero" are distinct concepts, the relationship between them is much closer than between any other sets and numbers. The cardinal numbers are equivalence classes of the sets. For any other cardinal number except "zero", the equivalence class of that number contains a huge number of sets, potentially infinite. For "zero", the equivalence class contains only a unique set, the empty set. Because of this one-to-one correspondence between the empty set and "zero", they may be interchanged in many contexts without causing any ambiguities.
  - kreetx 2y ago
    Right. What I was aiming at was that when someone invents one of these, they are probably thinking about the other, too, without the set theoretic rigor you recite.
adrian_b 2y ago
In Latin, "null" was not a noun (i.e. substantive), but an adjective applied to nouns. It was used in precisely the same word contexts as the words for "one", "two", "three" etc. and in those contexts you could substitute any cardinal numeral. Like any cardinal numeral, it could be used to answer questions about how many things are in a certain place. So it was really the number "zero". For the empty set, the most appropriate Latin word was the noun "nihil" ("nothing"), sometimes contracted to "nil" (with long "i") hence the NIL of LISP for the empty list. So the concepts of "zero" and "empty set" were distinguished in Latin and also in the other known ancient languages. Some modern programming languages use "null" in a wrong way, when they should have stuck to the NIL of LISP. A null integer or floating-point number denotes the quantity "zero", but a null pointer is not a quantity. A null pointer points to nothing, so it denotes the object NIL.
- badkitty99 2y ago
  [dead]
kazinator 2y ago
The word "null" in "null set" refers its Lebesgue measure being zero.
- badkitty99 2y ago
  Null sets in and of themselves have nothing to do with Lebesgue integrals. Null sets are definitely are not defined by Lebesgue integrals, you might be thinking of a set of measure zero which has to do with Lebesgue measure
  - deleted 2y ago
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  - kazinator 2y ago
    > has to do with Lebesgue measure As in, the only thing Lebesgue that my comment mentions.

In German, it's the same. I hope you are not talking about null in coding? Because I'm pretty sure human 2000 years ago did not know any programming code or even empty sets.

deleted 2y ago
[deleted]
rdtsc 2y ago
Empty set idea doesn’t seem so abstract. A bag of stuff can have nothing in it, so it’s empty. Combining and splitting up containers of items would have been an everyday occurrence.

kreetx 2y ago

I'm just nitpicking, but it's unlikely that the inventors of both had empty set and zero formalized to a degree to make them distinct.

adrian_b 2y ago
While the empty set and the number "zero" are distinct concepts, the relationship between them is much closer than between any other sets and numbers. The cardinal numbers are equivalence classes of the sets. For any other cardinal number except "zero", the equivalence class of that number contains a huge number of sets, potentially infinite. For "zero", the equivalence class contains only a unique set, the empty set. Because of this one-to-one correspondence between the empty set and "zero", they may be interchanged in many contexts without causing any ambiguities.
- kreetx 2y ago
  Right. What I was aiming at was that when someone invents one of these, they are probably thinking about the other, too, without the set theoretic rigor you recite.

adrian_b 2y ago

In Latin, "null" was not a noun (i.e. substantive), but an adjective applied to nouns. It was used in precisely the same word contexts as the words for "one", "two", "three" etc. and in those contexts you could substitute any cardinal numeral. Like any cardinal numeral, it could be used to answer questions about how many things are in a certain place. So it was really the number "zero". For the empty set, the most appropriate Latin word was the noun "nihil" ("nothing"), sometimes contracted to "nil" (with long "i") hence the NIL of LISP for the empty list. So the concepts of "zero" and "empty set" were distinguished in Latin and also in the other known ancient languages. Some modern programming languages use "null" in a wrong way, when they should have stuck to the NIL of LISP. A null integer or floating-point number denotes the quantity "zero", but a null pointer is not a quantity. A null pointer points to nothing, so it denotes the object NIL.

badkitty99 2y ago
[dead]

kazinator 2y ago

The word "null" in "null set" refers its Lebesgue measure being zero.

badkitty99 2y ago
Null sets in and of themselves have nothing to do with Lebesgue integrals. Null sets are definitely are not defined by Lebesgue integrals, you might be thinking of a set of measure zero which has to do with Lebesgue measure
- deleted 2y ago
  [deleted]
- kazinator 2y ago
  > has to do with Lebesgue measure As in, the only thing Lebesgue that my comment mentions.