Theorem formulation "Given ..., then ..." or "For all ..., ..."? When formulating a theorem, which of the following forms would be preferred, and why? Or is there another even better formulation? Are there reasons for or against mixing them in one paper?
Formulation 0: If $x\in X$, then (expression involving $x$).
Formulation 1: Given $x$ in $X$, then (expression involving $x$).
Formulation 2: For all $x$ in $X$ it holds that (expression involving $x$).
 A: Formulation 0 confounds the binding of the symbol $x$ as a variable to $X$ with set inclusion $x\in X$.
The other two formulations are equivalent, but the second seems stronger and is more verbose, so for now I prefer Formulation 2.
A: I guess I'm a simpleton, I always preferred a theorem stated memorably:
Theorem 1. Even numbers are interesting.
Compared to...
Theorem 2. If $x$ is an even number, then $x$ is interesting.
...which is long-winded; or...
Theorem 3. Given an even number $x$, $x$ is interesting.
Theorem 3 also has odd consonance (writing "...$x$, $x$ is ..." seems like bad style).
Theorem 4. For all even numbers $x$, we have $x$ be interesting.
This also suffers from peculiar consonance ("we have $x$ be interesting" is quite alien, despite being proper grammar).
Theorem 1 has a quick and succinct enunciation ("Even numbers are interesting"), the proof can begin with a specification "Let $x$ be an even number. Then [proof omitted]." 
Also we see theorem 1 has additional merit: it avoids needless symbols.
There is one warning I should give: each theorem is different. Some theorems can be stated beautifully without symbols (e.g., theorem 1). Others cannot be coherently stated without symbols. There is not "iron law" on how theorems should be formulated; it's a case-by-case problem. 
