A Collection of Numbers Whose Proof of Irrationality Is Like that of the Number "e"

Autor/inn/en	Osler, Thomas J.; Stugard, Nicholas
Titel	A Collection of Numbers Whose Proof of Irrationality Is Like that of the Number "e"
Quelle	In: Mathematics and Computer Education, 40 (2006) 2, S.103-107 (5 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0730-8639
Schlagwörter	Geometric Concepts; Transformations (Mathematics); Calculus; Number Concepts; Mathematical Logic; Validity + Suchen Sie Ihr Suchwort? Elementare Geometrie; Transformationstheorie; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Number concept; Zahlbegriff; Mathematical logics; Mathematische Logik; Gültigkeit
Abstract	In some elementary courses, it is shown that square root of 2 is irrational. It is also shown that the roots like square root of 3, cube root of 2, etc., are irrational. Much less often, it is shown that the number "e," the base of the natural logarithm, is irrational, even though a proof is available that uses only elementary calculus. In this short note, the authors repeat this proof and find a collection of other numbers that can be proved to be irrational in a similar way. While this work is not new, the presentation here is simpler than others. It is appropriate for students in calculus, advanced calculus and real analysis. (ERIC).
Anmerkungen	MATYC Journal Inc. Mathematics and Computer Education, P.O. Box 158, Old Bethpage, NY 11804. Tel: 516-822-5475; Web site: http://www.macejournal.org
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10