What letter is the empty set symbol ∅ to you?
elementary set theory - Which symbol should be used for an empty set? - Mathematics Stack Exchange
elementary set theory - Name of symbol of null set. - Mathematics Stack Exchange
What does the hollow dot mean?
In a lot of contexts, the hollow dot would mean function composition, but I'm inclined to think this is a typographical issue. The problem reads like somebody was trying to write up an equation that they want you to solve, and the symbols aren't being displayed correctly.
Can I take a wild guess and ask if this problem was presented via some sort of web-assignment system? Like, say, MyMathLab?
Try this: replace the commas with plus signs, and replace the hollow dot with an equals sign. Does the result look like the sort of problem you've been studying? If so, I would suggest trying to solve that, then bringing the issue to your instructor's attention-- if you're having this issue, so are others, and your instructor needs to be aware of this.
Best of luck!
More on reddit.comWhat is a non-empty set?
Any set with at least one element is a non-empty set.
What is an empty set example?
Why is an empty set called a set?
We know that a set is a collection of well-defined objects. However, if we define a set using conditions that are not satisfied by any real number, the set will have no elements. If you subtract a set from itself, you will get A - A, which is a set with nothing in it. If the intersection of two sets A and B, since it is possible that A and B have no elements in common (for example, if A is the even integers and B is the odd integers). To define such sets, you need the empty set.
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I would say the following should be not too controversial:
and
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
(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
, 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
and
.
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
According to Wikipedia André Weil (and maybe others) introduced the symbol $\emptyset$ for the empty set. They were inspired by the letter Ø in the Norwegian and Danish alphabet. So, I guess you could argue that the symbol should be pronounced as it is pronounced in these alphabets.
In my experience most mathematicians just call the symbol "empty set".
Note also, that the Wikipedia article says that the symbol is not to be confused with the Greek letter $\phi$ or $\Phi$.
Although not mathematics, I thought I would add that in the APL programming language the empty vector is represented by the symbol ⍬, which is pronounced "zilde".
