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Mathematical Real Analysis Questions You have to answer two questions in order to get a thumb's...

Mathematical Real Analysis Questions

You have to answer two questions in order to get a thumb's up and good

Q.1  Let A = (0,2]. Prove that A does not have a minimum. What is the infimum of A?

Q.2. Theorem. Given any two real numbers x < y, there exists an irrational number satisfying x <t< y.
Proof. It follows from x < y that x−√2 < y−√2. Since Q is dense in R, there exists p ∈Q such that x−√2 < p < y−√2. Consequently··· (complete the proof.)

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