Abstract
For a set M, let \({\text {seq}}(M)\) denote the set of all finite sequences which can be formed with elements of M, and let \([M]^2\) denote the set of all 2-element subsets of M. Furthermore, for a set A, let 
denote the cardinality of A. It will be shown that the following statement is consistent with Zermelo–Fraenkel Set Theory \(\textsf {ZF}\): There exists a set M such that 
and no function 
is finite-to-one.
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References
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Halbeisen, L. A weird relation between two cardinals. Arch. Math. Logic 57, 593–599 (2018). https://doi.org/10.1007/s00153-017-0594-z
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DOI: https://doi.org/10.1007/s00153-017-0594-z