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.
Videos
According to Wikipedia André Weil (and maybe others) introduced the symbol 
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 
or 
.
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".
The distinction between the empty set $\emptyset$ and the number $0$ is similar to that between NULL and ZERO. For example, the set of real solutions (or informally "the solution") to $x^2=-1$ is $\emptyset$, but the solution to $x^2=0$ is $0$.
In my mind there is no need for a concept like NULL in mathematics if you think of NULL as in NULL-pointers.
NULL in this sense is a technical necessity because you cannot un-define a variable: Once a variable has been assigned a value, a certain bit of memory is reserved for this variable and this memory is marked as re-usable only if the variable goes out of scope (simplified speaking).
You cannot say "The variable with this name doesn't exist anymore." without letting it go out of scope, because that would make language interpretation much more complicated without many benefits. Therefore, to indicate that the value of the variable has no meaning, one uses NULL.
What NULL stands for in the end depends upon the programming language: In some it is a special keyword, but in some it is also just a different name for the integer $0$.
You can assign an arbitrary value to NULL in mathematics as mentioned in the other replies ($\emptyset$, $0$, etc.) but as mathematics has nothing to do with memory allocation there is really no need for such a thing as NULL.
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?
My professor's slides use both, and I'm confused if they mean different things. In high school, we used the second representation of phi. Assuming the first one is also phi. I think.
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.
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Best regards,
Dan