Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53512#.VMcrXizQrzE Author(s) Wolfgang Mueckenheim * Affiliation(s) University of Applied Sciences, Augsburg, Germany . 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. KEYWORDS Series , Sequences , Limits , Definability of Real Numbers , Set Theory Cite this paper Mueckenheim, W. (2015) Sequences and Limits. Advances in Pure Mathematics , 5 , 59-61. doi: 10.4236/apm.2015.52007 . References [ 1 ] Mueckenheim, W. (2011) Mathematik für die ersten Semester. 3rd Edition, Oldenbourg Verlag GmbH, Muenchen, 193. http://www.ama...
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