symbol denoting the empty set
Factsheet
notation - What is the mathematical symbol for "nothing"? - Mathematics Stack Exchange
How can I type the null sign?
How can I type the null sign?
How do you write the null symbol or slashed zero without confusion in Norwegian/Danish?
This is sufficiently rare, and handled in sufficiently many different ways, that you should always state explicitly how you're treating it. In my experience, the most common symbols are:
, 
, 
or similar on the more computer-sciencey side, and
or 
on the more logicy side.- Note that "
" is also used to denote contradiction, and "
" is also used as a predicate to denote "is undefined" or "doesn't halt" with "
" denoting "is defined"/"does halt."
- Note that "
But again, I'd explicitly state which you're using - although admittedly multiple of these would almost certainly make it obvious from context.
You can use some kind of Many-valued logic, but you said you want to put it simply. In SQL there is 3-valued logic with "null"/"unknown", for example.
Another suggestion is you can also type: Alt + 0216.
Best regards,
Dan
Hi! I'm Dan! An Independent Advisor and also a Microsoft user for several years. I'll be more than happy to assist you today!
Method 1:
The ∅ symbol can be entered by going into "Symbols", choose "Mathematical Characters" and from the dropdown "Subset".
Method 2:
Type 2205 and then press "Alt + X".
I hope this information is helpful. Please keep me updated on the status of this issue. If you have any more questions, feel free to ask and I will be glad to assist you.
Standard Disclaimer: There are links to non-Microsoft websites. The pages appear to be providing accurate, safe information. Watch out for ads on the sites that may advertise products frequently classified as a PUP (Potentially Unwanted Products). Thoroughly research any product advertised on the sites before you decide to download and install it.
Best regards,
Dan
Another suggestion is you can also type: Alt + 0216.
Best regards,
Dan
Hi! I'm Dan! An Independent Advisor and also a Microsoft user for several years. I'll be more than happy to assist you today!
Method 1:
The ∅ symbol can be entered by going into "Symbols", choose "Mathematical Characters" and from the dropdown "Subset".
Method 2:
Type 2205 and then press "Alt + X".
I hope this information is helpful. Please keep me updated on the status of this issue. If you have any more questions, feel free to ask and I will be glad to assist you.
Standard Disclaimer: There are links to non-Microsoft websites. The pages appear to be providing accurate, safe information. Watch out for ads on the sites that may advertise products frequently classified as a PUP (Potentially Unwanted Products). Thoroughly research any product advertised on the sites before you decide to download and install it.
Best regards,
Dan
So in math, I've always been taught to write my zeros with a small slash through them to differentiate between them and the letter O. Also, there's the symbol "∅" which denotes the empty set and is called the 'null sign'. If you are doing math in Norwegian or Danish, how do you avoid confusing the letter ∅ with these symbols?
I would say the following should be not too controversial:
$\emptyset$ and $\varnothing$ are typographical variants of the same mathematical symbol designating the empty set
The symbol was introduced by Bourbaki, was inspired by the Norwegian character Ø, but is a distinct character from it
The intention was most probably to create a symbol related to $0$ (zero), not to O (Oh), distinguished from it by striking it through. After all the empty set has all kinds of relations with the number $0$, but none with the letter O. (By contrast big-Oh and little-o symbols derive from the word "order".)
The symbol has absolutely no relation (apart from appearance) with the lower-case Greek letter phi, with typographical variants $\phi$ and $\varphi$.
There is a webpage where you can find mention of this: http://jeff560.tripod.com/set.html
Here's an extract
The null set symbol (Ø) first appeared in N. Bourbaki Éléments de mathématique Fasc.1: Les structures fondamentales de l'analyse; Liv.1: Theorie de ensembles. (Fascicule de resultants) (1939): "certaines propriétés... ne sont vraies pour aucun élément de E... la partie qu’elles définissent est appelée la partie vide de E, et designée par la notation Ø." (p. 4.)
André Weil (1906-1998) says in his autobiography that he was responsible for the symbol:
Wisely, we had decided to publish an installment establishing the system of notation for set theory, rather than wait for the detailed treatment that was to follow: it was high time to fix these notations once and for all, and indeed the ones we proposed, which introduced a number of modifications to the notations previously in use, met with general approval. Much later, my own part in these discussions earned me the respect of my daughter Nicolette, when she learned the symbol Ø for the empty set at school and I told her that I had been personally responsible for its adoption. The symbol came from the Norwegian alphabet, with which I alone among the Bourbaki group was familiar.
The citation above is from page 114 of André Weil's The Apprenticeship of a Mathematician, Birkhaeuser Verlag, Basel-Boston-Berlin, 1992. Translated from the French by Jennifer Gage. The citation was provided by Julio González Cabillón.
You should also note that Nicolas Bourbaki is a collective pseudonym for a group of French-speaking mathematicians.
Concerning your question, I remember one of my math professor telling us that in fact, it was a claim by both André Weil and Claude Chevalley, but I can't find the citation for Chevalley.
I've found also this lecture about history of math from a Canadian University (in French), where this issue is mentioned: http://www.mat.ulaval.ca/fileadmin/Cours/MAT-2500/Bourbaki.pdf