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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 $x$).

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    I used the 'proof-writing' tag because no other tag I found seemed appropriate, and I cannot create new ones.2012-03-21
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    They're all equivalent. Use what reads best. If you can give a concrete example, perhaps we can help you choose.2012-03-21
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    @lhf: I've added an extra subquestion regarding mixing them in one paper.2012-03-21
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    Why not examine a few papers you like, and see what is done there? Then see if you can tell *why* you like them.2012-03-21
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    "For all $x$ in $X$ it holds that $\dots$" sounds to me like something transliterated from a language other than English.2012-03-21

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