The Instructor's Guide to Real Induction

• Published in 2012
• Added on 2019-03-02

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.

Links

• http://arxiv.org/abs/1208.0973v1
• http://arxiv.org/pdf/1208.0973v1

Other information

BibTeX entry

@article{TheInstructorsGuidetoRealInduction,
	key = {TheInstructorsGuidetoRealInduction},
	type = {article},
	title = {The Instructor's Guide to Real Induction},
	author = {Pete L. Clark},
	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.},
	comment = {},
	date_added = {2019-03-02},
	date_published = {2012-10-09},
	urls = {http://arxiv.org/abs/1208.0973v1,http://arxiv.org/pdf/1208.0973v1},
	collections = {About proof,Easily explained,Fun maths facts,The act of doing maths},
	url = {http://arxiv.org/abs/1208.0973v1 http://arxiv.org/pdf/1208.0973v1},
	year = 2012,
	urldate = {2019-03-02},
	archivePrefix = {arXiv},
	eprint = {1208.0973},
	primaryClass = {math.HO}
}