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hey everybody im bill kinney and this is my real analysis exam 1 review problems and solutions video if youre looking for some introductory lectures about real analysis i would encourage you to check out my playlist in the description below in this video were going to go through a bunch of foundational definitions theorem statements true false questions and a bunch of proofs related to the basics of real analysis for example that you could find in the first couple chapters of this book by russell gordon its only later in the semester that were going to get into heavier duty content about topology and metric spaces for example like you can find in chapter 2 of baby rudin so were going to start with some definitions here let s be a non-empty set of real numbers that is bounded above so on the real number line theres some upper bound for s theres some number call it capital m say perhaps really big such that every element of s is less than or equal