Editing Tarski's theorem about choice (section)

{{Short description|Theorem equivalent to the Axiom of Choice}}
In [[mathematics]], '''Tarski's theorem''', proved by {{harvs|txt|first=Alfred|last= Tarski|authorlink=Alfred Tarski|year=1924}}, states that in [[Zermelo–Fraenkel set theory|ZF]] the theorem "For every infinite set <math>A</math>, there is a [[bijective map]] between the sets  <math>A</math> and <math>A\times A</math>" implies the [[axiom of choice]]. The opposite direction was already known, thus the theorem and axiom of choice are equivalent.

Tarski told {{harvs|first=Jan|last=Mycielski|authorlink=Jan Mycielski|year=2006|txt}} that when he tried to publish the theorem in ''[[Comptes Rendus de l'Académie des Sciences de Paris]]'', [[Maurice René Fréchet|Fréchet]] and [[Henri Lebesgue|Lebesgue]] refused to present it. Fréchet wrote that an implication between two well known propositions is not a new result. Lebesgue wrote that an implication between two false propositions is of no interest.