Use curly brackets for sets

In a recent assignment, I saw a student who used parentheses (round brackets) to represent a set: $$(1,2,3,\cdots ).$$ Of course, as Georg Cator put it, "the essence of mathematics lies in its freedom," so it is OK to use whatever symbols to represent a set, if you define it first, consistently. However, using parentheses for sets is unconventional. We conventionally use curly brackets instead: $$\{1,2,3,\cdots \}$$ I recommend you stick to this convention to avoid any confusion.

By the way, a list of elements enclosed by parentheses, such as in $(1,2,3)$, is often used to represent a tuple. A tuple is an ordered list of elements. As such, $(1,2,3)$ and $(2,1,3)$, for example, represent different tuples. By comparison, in sets, the order of elements does not matter so that $\{1,2,3\}$ and $\{2,1,3\}$ represent the same, identical set. Furthermore, redundant elements are allowed in tuples. That is, $(1,1,2)$ is a valid tuple, whereas $\{1,1,2\}$ is not a valid set because the two "1" are not distinguishable (or it should be treated as $\{1,2\}$ by removing the redundancy).