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Math · Advanced Math
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jonnaniplication : For all x, y, k E R, k 0: If k·x k-y, then x = y. 15. Use The Multiplicative Property of Zero to prove that 0 cannot have a multiplicative inverse. Hint: Use Proof by Contradiction: Suppose 0 has a multiplicative inverse x. .. Prove The Uniqueness of Additive Inverses: Suppose x e R. If w eR is any real number with the property that x + w-0-w+ x, then w = x. In other words,-x is the only real number that satisfies the above equations. 16. 17. Use the previous Exercise to show that -0 0. Hint: which Field Axiom tells us what 0+0 is? of Additive Inverses to prove that for all R:1).x. Hint: simplify(-1).x. The Double Negation Property: Use some of the previous Exercises to s 19. how that: For all x E R: 0. If y E R is any 1/x. In other 1/x is the only real 20. Prove The Uniqueness of Multiplicative Inverses: Suppose x E R and x real number with the property that x.y 1-y .x, then y number that satisfies the above equations. 19 Sets, Axioms, Theorems&Proofs 20 please
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