The Sermelo axiom or selection principle affirms that there is a function that opposes one of its elements to a class of non-empty sets. In other words, the Sermelo axiom presupposes that one element can be taken from every set of any system consisting of non-empty sets.
The Sermelo axiom was expressed by Sermelo in 1904. Sermelo was based on this axiom when proving the theorem about the complete ordering of each set. The Sermelo axiom has caused great controversy among mathematicians. A number of mathematicians do not accept it, so they do not admit that every single unit can be fully ordered.
However, the proof of many theorems of classical mathematical analysis is in some sense based on the Sermelo axiom.
Instead of the Sermelo axiom, they now use the Sorn lemma, which is equivalent to it and is more suitable for use.
Source: Misir Mardanov, Sabir Mirzoyev, Shabala Sadigov, The book “The mathematical explanatory dictionary of pupils”, Baku, 2016.

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