Abstract
In real analysis, a facility for working with the supremum of a bounded set, the limit of a sequence, and the ε-δ definitions of continuity is essential for a student to be successful. Many students stumble when first asked to compose proofs using these core definitions. This chapter is designed to better prepare students and allow them to overcome these initial hurdles. We present proof strategies that explicitly show students how to deal with the fundamental definitions that they will encounter in real analysis; followed by numerous examples of proofs that use these strategies.
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Notes
- 1.
This inequality is also called the reverse triangle inequality.
- 2.
The algebraic “trick,” of adding and subtracting the same value, is used often in analysis.
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Cunningham, D.W. (2013). Core Concepts in Real Analysis. In: A Logical Introduction to Proof. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3631-7_9
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DOI: https://doi.org/10.1007/978-1-4614-3631-7_9
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