In mathematics, Wetzel's problem concerns bounds on the cardinality of a set of analytic functions that, for each of their arguments, take on few distinct values.
[3] Paul Erdős in turn learned about the problem at the University of Michigan, likely via Lee Albert Rubel.
[4] However, as Erdős showed, the situation for countable sets is more complicated: the answer to Wetzel's question is yes if and only if the continuum hypothesis is false.
One direction of this equivalence was also proven independently, but not published, by another UIUC mathematician, Robert Dan Dixon.
As Ashutosh Kumar and Saharon Shelah later proved, both positive and negative answers to this question are consistent.