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  1. H

    Real analysis question

    Well, the text says that "A is the set of ALL positive rationals p such that p^2<2". So a) p in A implies p^2-2<0 by definition and b) you can't say A={5} or something similar.
  2. H

    Real analysis question

    When it comes to the form of (3), I suppose it's just a clever choice, such that q gets the properties we want. However, we know that p^2<2 and p^2>2 give distinct cases, so a factor of p^2-2 somewhere in the expression is to be expected. Similarly, the term linear in p is suggested by the...
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