Quote:
Originally Posted by ntvy95
Instead of choosing  or  explicitly, the proof let the choice for the value of  depends on the value of  :  , because for whatever the real value of  is,  only has value of 1 or -1, hence  or  . In my understanding, this dependence does not make the chosen dichotomy invalid.
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That's the point. This part is crucial: "the proof let the choice for the value of

depends on the value of

". The only certain correlation is

. How do we know (definition, theorem, lemma,...) that

works the same as

? IMHO it cannot be drawn from the

, (where not all

coefficients are zeros).