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...Advanced calculus notes david wright january contents preliminaries tools for analysis these are from my spring course this was taught by dr sona swanson at ucf out of fitzpatrick s nd ed in order to rigorously develop one needs understand the foundation on which it is constructed r we will assume that eld real numbers satises three groups axioms field positivity and completeness axiom commutativity addition a b associativity c additive identity x inverse multiplication ab ba bc multiplicative all other than have t call distributive property ac nontrivial assumption i e p any exactly or unless properties inequalities using can establish following familiar each if then ordering dene similarly put into words greater sum positive zero they equal denition inductive set said be number ex natural n intersection subsets remark thereisaninteresting consequence follows identically what about mathematical induction mathematicalinduction lets beamathematicalpropertyorassertion wheren suppose true...