E(X) and the Equality of Expectation: Debunked or Confirmed?

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Is this true? In all cases?
 
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E(X) = expectation of X

Let X = {-1, 0, 1}
E(X) = (-1+0+1)/3 = 0

E|X| = ( |-1|+|0|+|1| )/3 = (1+0+1)/3 = 2/3

So, I think no, it's not true that E|X| = E(X) if I understand the question correctly.
 
I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
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