5. What are precautions taken while formulate the axioms?
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1. The anxioms should not contradict each other. They must be consistent.
2. We must create only necessary and sufficient number of anxioms for the development of structure. That is, we should not create more Anxioms that what is required.
3. The Anxioms created should be independent. That is no Anxiom should be created based on another Anxiom.
So, consistency, independence and completeness are the three important characteristics required for the Anxioms.
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