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This question might be rude or inappropriate, but I am very beginner of studying mathematics.
Today I had learned the concept of Axiom of Choice, which states that $ \forall$ nonempty indexed set $S_i$, there $\exists$ indexed family of element $x_i$ where $\forall x_i \in Si$.
To me, at first it reached out to me as a just mere fact, but can't understand why this axiom must have been accepted as an axiom.
It's little confusing to me.
To wrap up the notion of this OP, it could be summarized as below:
Why does the concept of axiom of choice must be accepted as axiom?
What makes a statement to be valued to be designated as an axiom?