Boundedly expressible sets

Jaroslav Hančl; Jan Šustek

Displaying similar documents to “Boundedly expressible sets”

Lucas balancing numbers

Kálmán Liptai (2006)

Acta Mathematica Universitatis Ostraviensis

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A positive $n$ is called a balancing number if $1 + 2 + \dots + (n - 1) = (n + 1) + (n + 2) + \dots + (n + r) .$ We prove that there is no balancing number which is a term of the Lucas sequence.

Triangular repunit-there is but 1

John H. Jaroma (2010)

Czechoslovak Mathematical Journal

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In this paper, we demonstrate that 1 is the only integer that is both triangular and a repunit.

On the metric dimension of converging sequences

Ladislav, Jr. Mišík, Tibor Žáčik (1993)

Commentationes Mathematicae Universitatis Carolinae

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In the paper, some kind of independence between upper metric dimension and natural order of converging sequences is shown — for any sequence converging to zero there is a greater sequence with an arbitrary ( $⩽ 1$ ) upper dimension. On the other hand there is a relationship to summability of series — the set of elements of any positive summable series must have metric dimension less than or equal to $1 / 2$ .