Interesting Esoterica

The Instructor's Guide to Real Induction

Article by Pete L. Clark
  • Published in 2012
  • Added on
We introduce real induction, a proof technique analogous to mathematical induction but applicable to statements indexed by an interval on the real line. More generally we give an inductive principle applicable in any Dedekind complete linearly ordered set. Real and ordered induction is then applied to give streamlined, conceptual proofs of basic results in honors calculus, elementary real analysis and topology.

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BibTeX entry

@article{TheInstructorsGuidetoRealInduction,
	title = {The Instructor's Guide to Real Induction},
	abstract = {We introduce real induction, a proof technique analogous to mathematical
induction but applicable to statements indexed by an interval on the real line.
More generally we give an inductive principle applicable in any Dedekind
complete linearly ordered set. Real and ordered induction is then applied to
give streamlined, conceptual proofs of basic results in honors calculus,
elementary real analysis and topology.},
	url = {http://arxiv.org/abs/1208.0973v1 http://arxiv.org/pdf/1208.0973v1},
	year = 2012,
	author = {Pete L. Clark},
	comment = {},
	urldate = {2019-03-02},
	archivePrefix = {arXiv},
	eprint = {1208.0973},
	primaryClass = {math.HO},
	collections = {about-proof,easily-explained,fun-maths-facts,the-act-of-doing-maths}
}