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Results tagged with axiom-of-choice
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user 1631
An important and fundamental axiom in set theory sometimes called Zermelo's axiom of choice. It was formulated by Zermelo in 1904 and states that, given any set of mutually disjoint nonempty sets, there exists at least one set that contains exactly one element in common with each of the nonempty sets. The axiom of choice is related to the first of Hilbert's problems.
8
votes
Accepted
Subset of the plane that intersects every line exactly twice
By AC, choose a cardinal well-ordering of the lines in in the plane and any well-ordering of all the points.
We proceed by transfinite induction.
Suppose $A_l$ is a set of points, no three colinear, …
- 1,987