I Chernoff Bounds for Independent Bernoulli Sums

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What is wrong with this proof? Can you notice that? or I am wrong. In my opinion, in the R.H.S. of inequality (3.2), the index of 'e' must be positive if we use the proof. I also want to know how to derive the proof of inequality(3.3)? Author said it is similar to that of (3.2). But I don't understand that.
Chernoffbounds proof.png
 
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I cleared my doubt taking suitable guidelines from other statistician on Internet.
 

Thread 'Deductive proof in logic formal systems'

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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