| 11. | The non-finitistic constructions show up in the interpretation of mathematical induction.
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| 12. | The case of only finitely many terms can be proved by mathematical induction.
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| 13. | Mathematical induction is a form of direct proof, usually done in two steps.
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| 14. | He proved the associative and commutative properties, among others, through mathematical induction.
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| 15. | The proof is by mathematical induction on the exponent " n ".
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| 16. | He did make repeated use of mathematical induction, introducing the method of infinite descent.
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| 17. | The general proof proceeds by mathematical induction.
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| 18. | This can be shown by mathematical induction.
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| 19. | He also used the two basic concepts of mathematical induction, though without stating them explicitly.
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| 20. | By the principle of mathematical induction it follows that the result is true for all natural numbers.
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