And if no, why not?
And if no, why not?
Because it's not empty.
eDIT: I'm not a mathematician, so if somebody wants to come along and tell me I'm wrong, please do so.
Anyway, think of it like this. The set can be thought of as a room. Inside the room, there is a box, but the box is empty. This is {0}. If there were something in the box, say one rock, it would be {1}. If there were two empty boxes, it would be {0,0}. If you climbed inside one of the boxes, it would be {0,you being silly}. Etc. Get it? It's all boxes.
Secret forum
It's just a symbol. If you define {0} as an empty set, you can write it that way. However, it can be argued that {0} is a set with one element which has a real value of 0.
Best to be explicit.
"If you're not part of the solution, you're part of the precipitate." ~Henry J. Tillman
0 is not in the set of positive integers, or the set of letters {A,B,C,Z}. By putting 0 in the set by default, you are confining the parameters of your set.
If you're familiar with arrays, an empty set correlates to an array with size zero, and {0} is an array with size 1 and that element having a value of 0.
"If you're not part of the solution, you're part of the precipitate." ~Henry J. Tillman
Like I said, if you write something along the lines of:
Let {0} represent the empty set
then it's fine. But why would you want to represent a simple idea in an unconventional and paradoxical way except to obfuscate the intent of your work?
Don't get me wrong, someone reading your work will might know what you mean when you write {0} without a definition, but this assumption should not be made.
"If you're not part of the solution, you're part of the precipitate." ~Henry J. Tillman