Transcription of KEY CONCEPTS: Introduction to Real Analysis
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KEY CONCEPTS: Introduction to Real Analysis
KEY CONCEPTS: Introduction to RealAnalysisSamvel Atayan and Brent HickmanSummer 20081 Sets and FunctionsPRELIMINARY NOTE: Many definitions given in these notes are framed interms specific to the real numbers. This simplifies matters greatly becauseof the familiar ordering and distance concepts which come asstandard fea-tures in (finite-dimensional) Euclidean space. However, many of the conceptsgiven below have useful analogs in more exotic spaces ( , spaces of func-tions or spaces of infinite sequences), but those require some knowledge ofmetric topology, which will be a major emphasis of your Economic Analysis I(06E:200) class. For the purpose of math camp, we will resignourselves tothe quaint shackles of Euclidean SetsDefinition 1 Asetis a collection of elements. If an elementxis in a setAthen we denotex A,ifxis not inA,then we writex / A If every element of a setAis also in setB, thenAis a subset ofBandwe denote this asA BorB A.
KEY CONCEPTS: Introduction to Real Analysis Samvel Atayan and Brent Hickman Summer 2008 1 Sets and Functions PRELIMINARY NOTE: Many definitions given in these notes are framed in
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