Using setminus notation with set elements The "correct" way to write a set without a specific element is as follows: $S \setminus \{s\}$
But in some contexts this is cumbersome to write/type or read, and it detracts from the flow of the writing. Is it acceptable to just use $S \setminus s$?
Edit: By "cumbersome" i mean they look bad when you're trying to inline formulas in LaTeX.
 A: If you have to write this many times in a piece of text, and there is no possibility of confusion of $s$ being an actual set of elements you are removing, it is okay to first write one sentence reminding the reader of this abuse of notation ("In the following, we write $S\setminus s$ to mean $S \setminus \{s\}$") and then write $S \setminus s$ thereafter. But otherwise I would recommend using the proper notation.
A: It really depends on the context. 
For a lot of mathematics, I would agree with Brian M. Scott: in stuff like elementary real/complex analysis (and similar some basic constructions in algebra), one almost always work only with objects and sets of objects. In these situations as Dan Petersen comments, there is already some "established notation" where the line between $\{x\}$ and $x$ are blurred, and abusing notation this way may be "marginally acceptable". 
For actually doing foundations stuff or set theory, then I agree with Mark Dominus. In a universe where everything is a set (or a proper class), and dealing with sets of sets and specifically power sets is common, you should absolutely not abuse notation like that. This is because if you define the set $y := \{ \{\}, x, \{x\}\}$, the two sets $y\setminus x$ and $y\setminus \{x\}$ are very different objects. 
In other words, before you abuse the notation, you have to justify why the notation can be abused. If you work in a context where sets are always collections of some primitive objects, where sets of sets are not considered, then you may be able to get away with this notation by virtue of being able to identify $x$ with $\{x\}$. By in general I would advise against doing something like that. 
A: To answer your question, no, that is not acceptable; readers will be puzzled, or confused, and perhaps annoyed.
If you the braces really bother you, you can define a new operator.  Say something like "We define $S\dot-x$ to be an abbreviation for $S\setminus\{x\}$". People might raise an eyebrow at that, but not as much as if you overload $\setminus$ the way @Ted suggested above, and nobody is likely to describe it as "an abuse of notation".
