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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...

Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=51184#.VFsmlmfHRK0 Author(s)   Rahman Khatibi Affiliation(s) Consultant Mathematical Modeller, Swindon, UK . ABSTRACT New operators are presented to introduce “arithmetic calculus”, where 1) the operators are just obvious mathematical facts, and 2) arithmetic calculus refers to summing and subtracting operations without solving equations. The sole aim of this paper is to make a case for arithmetic calculus, which is lurking in conventional mathematics and science but has no identity of its own. The underlying thinking is: 1) to shift the focus from the whole sequence to any of its single elements; and 2) to factorise each el...

Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=48885#.VDcwKVfHRK0 Author(s)    Jana Fialová , Ladislav Mišk , Oto Strauch Affiliation(s) Mathematical Institute, Slovak Academy of Sciences, Bratislava, Slovakia . Department of Mathematics, University of Ostrava, Ostrava, Czech Republic . Mathematical Institute, Slovak Academy of Sciences, Bratislava, Slovakia . ABSTRACT In this paper, we apply the Weyl's limit relation to calculate the limit ,  where γ q ( n ) is the van der Corput sequence in base q, g ( x , y , z), is the asymptotic distribution function of ( γ q ( n ), γ q ( n + 1 ), γ q ( n + 2 )), and F ( x , y , z) = max ( x , y , z ), min ( x , y , z), and xy z, respectivel...