Abstract
We believe that the ZF–axioms describe in a correct way our intuitive contemplations concerning the notion of set. The axiom of choice (AC) is intuitively not so clear as the other ZF–axioms are, but we have learned to use it because it seems to be indispensable in proving mathematical theorems. On the other hand the (AC)has “strange” consequences, such as “every set can be well–ordered” and we are unable to “imagine” a well–ordering of the set of real numbers.
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© 2006 Springer-Verlag Berlin/Heidelberg
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Herrlich, H. (2006). Choice Principles. In: Axiom of Choice. Lecture Notes in Mathematics, vol 1876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-34268-0_2
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DOI: https://doi.org/10.1007/3-540-34268-0_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30989-5
Online ISBN: 978-3-540-34268-7
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