TITLE:
Sequences and Limits
AUTHORS:
Wolfgang Mueckenheim
KEYWORDS:
Series, Sequences, Limits, Definability of Real Numbers, Set Theory
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.5 No.2,
January
26,
2015
ABSTRACT: It is widely held that irrational numbers can be represented by infinite digit-sequences. We will show that this is not possible. A digit sequence is only an abbreviated notation for an infinite sequence of rational partial sums. As limits of sequences, irrational numbers are incommensurable with any grid of decimal fractions.