Talks in the Department of Mathematics
Friday, April 19th, 3:15 p.m., 219
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.