| 1. | Let I be an inductive set guaranteed by the Axiom of Infinity.
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| 2. | One such system is ZFC with the axiom of infinity replaced by its negation.
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| 3. | Similarly with the higher axioms of infinity.
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| 4. | Therefore its existence is taken as an axiom & mdash; the axiom of infinity.
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| 5. | His arguments only indicate that it cannot justify the axioms of infinity and power set.
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| 6. | For existence, we will use the Axiom of Infinity combined with the Axiom schema of specification.
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| 7. | I wonder, how and where-the axiom of infinity must be used by Computer science.
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| 8. | Moreover, NFU remains relatively consistent when augmented with an axiom of infinity and the axiom of choice.
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| 9. | In some formulations of ZF, the axiom of empty set is actually repeated in the axiom of infinity.
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| 10. | Besides the axioms of infinity and power set, the axioms of pairing were used in the modern argument.
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