%0 Journal Article %T Sequences and Limits %A Wolfgang Mueckenheim %J Advances in Pure Mathematics %P 59-61 %@ 2160-0384 %D 2015 %I Scientific Research Publishing %R 10.4236/apm.2015.52007 %X 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. %K Series %K Sequences %K Limits %K Definability of Real Numbers %K Set Theory %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53512