Miami University

Talks in the Department of Mathematics

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Algebra Seminar
Friday, April 19th, 3:15 p.m., 219 Bachelor.

Luise-Charlotte Kappe, SUNY Binghamton.

Cantor's Diagonalization Revisited: Constructing Transcendental Numbers.

Abstract: An evolving awareness of the deep nature of the real numbers began over 2,500 years ago, when the Pythagoreans were startled by their discovery that numbers such as the square root of 2 were not rational. A recurring theme in their history is that the set of real numbers is richer and much more complex than is generally assumed. The demonstration by Cantor, that the reals cannot be enumerated, is a well-known landmark of these developments. Knowing that the rationals can be enumerated, it follows from Cantor's diagonalization that there exist irrational numbers. Similarly, knowing that the algebraic numbers can be enumerated, it follows that there exist transcendental numbers.
But can one use Cantor's diagonalization for the construction of such numbers? The topic of this talk is the explicit construction of a transcendental number using Cantor's diagonalization. 



Department Colloquium

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