@utabintarbo: Just said that about religion as a precaution. In your quote of a definition of an axiom:
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It doesn't rest upon anything in order to be valid
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I disagree, you can take axioms that need other axioms to define things, but cannot be proven from that. Also note that some axioms can either be taken as axiom, or as proof from other (stronger)axioms; and there is also equivilence. I would instead say "Axioms are not proven from anything to be valid", although sometimes internal consistentcy is not obvious.
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A true axiom can not be refuted because the act of trying to refute it requires that very axiom as a premise.
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An aspect of logic; A=> not A is a proof that A is false by self-contradiction. An axiom that self-contradicts isnt much use
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BTW Asides: I hardly encountered all my axioms in secondary classes; My profile reads: bothed physics student. In fact, i did some extra math on the side, and my first 2.5years i were a perfectly good student. (I am taking a in-between year to maybe be one again.)