Displaying similar documents to “On the generalized limit of bounded sequences”

Multigeometric sequences and Cantorvals

Artur Bartoszewicz, Małgorzata Filipczak, Emilia Szymonik (2014)

Open Mathematics

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For a sequence x ∈ l 10, one can consider the achievement set E(x) of all subsums of series Σn=1∞ x(n). It is known that E(x) has one of the following structures: a finite union of closed intervals, a set homeomorphic to the Cantor set, a set homeomorphic to the set T of subsums of Σn=1∞ x(n) where c(2n − 1) = 3/4n and c(2n) = 2/4n (Cantorval). Based on ideas of Jones and Velleman [Jones R., Achievement sets of sequences, Amer. Math. Monthly, 2011, 118(6), 508–521] and Guthrie and Nymann...

Individual choice sequences in the work of L. E. J. Brouwer

Joop Niekus (2005)

Philosophia Scientiae

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Choice sequences are sequences not completely determined by an algorithmic law. We maintain that the introduction of particular choice sequences by Brouwer in the late twenties was not recognised as such. We claim that their later use in the method of the creative subject was not traced back to this original usage and has been misinterpreted. We show where these particular choice sequences appear in the work of Brouwer and we show how they should be handled.