As you have read, axioms are mathematical statements that are assumed to be true and taken without proof. Use complete sentences to describe why a proof would need to have axioms to build on.
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axioms are the statements which are true and don't need to be defined. When we are given to prove something we take these axioms and other previously proved statements as reference. Behind every proof there must be a universal truth which needs to be defined most often. So using axioms while proving something is necessary.
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