MATH 451 Study Guide - Final Guide: Root Test, Convergent Series, Formal Proof
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N2 if n belongs to n, then its successor n+1 belongs to n. N3 1 is not the successor of any element in n. N4 if n and m in n have the same successor, then n=m. N5 subset n (sn), i) 1 s ii) if n s, then n+1 s then s=n (usually use proof by induction) * induction i) p1 is true ii) check pn is true, then check pn+1 is true. A1 a+ (b+c) = (a+b)+c for all a, b, c. A2 a+b = b+a for all a,b. A4 for each a, there is an element st a+(-a)=0. M1 a(bc) = (ab)c for all a,b,c. M4 for each a 0, there is an element st =1. Dl a(b+c) = ab+ac for all a,b,c. Def of absolute value: |a| = a if a 0 and |a| = -a if a 0. 3. 5 theorem: |a| 0 for all a in r. If i) ii) iii) iv) v) vi) vii)
