abstract
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A weird relation between two cardinals

Lorenz Halbeisen

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For a set M, let seq(M) denote the set of all finite sequences
which can be formed with elements of M, and let {M,M} denote
the set of all 2-element subsets of M.
It will be shown that the following statement is consistent
with Zermelo-Fraenkel Set Theory ZF: There exists a set M
such that the cardinality of seq(M) is strictly smaller than
the cardinality of {M,M} and no function from {M,M} to seq(M) is
finite-to-one.