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Please make your proofs concise. 1. If a<b, then a< (a+b)/2 < b 2. If I and J are open intervals, prove that either I∩ J =Ø orI∩ Jis also an open interval 3. Let x1, x2∈. If x1 is not equal to x2, then there exists ε1>0 and ε2>0 such that N(x1, ε1)∩N( x2, ε2) =Ø 4. Let β be a lower bound for...