Author(s)

Wolfgang Mueckenheim^*

University of Applied Sciences, Augsburg, Germany.

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.

Series, Sequences, Limits, Definability of Real Numbers, Set Theory

Mueckenheim, W. (2015) Sequences and Limits. Advances in Pure Mathematics, 5, 59-61. doi: 10.4236/apm.2015.52007.