There is no greatest negative real number. dentify which of the following is a negation for the statement and then fill in the blanks to prove the statement by contradiction. O There is no greatest negative real number. O There is no greatest positive real number. There is a greatest negative real number. O There is a least negative real number. O There is a greatest positive real number. Proof by contradiction: Suppose not. That is, suppose there is a greatest negative real number a ✓ x Then, by assumption, a < 0 Find a new real number, expressed in terms of a, that s both negative and greater than a. Use this expression to fill in the blank in the following inequality. a <2a <0 and, for every negative real number x, a > x This result contradicts the assumption that a is the greatest negative real number ✓ ✓ Therefore the supposition is false and the given statement is true.

There is no greatest negative real number. dentify which of the following is a negation for the statement and then fill in the blanks to prove the statement by contradiction. O There is no greatest negative real number. O There is no greatest positive real number. There is a greatest negative real number. O There is a least negative real number. O There is a greatest positive real number. Proof by contradiction: Suppose not. That is, suppose there is a greatest negative real number a ✓ x Then, by assumption, a < 0 Find a new real number, expressed in terms of a, that s both negative and greater than a. Use this expression to fill in the blank in the following inequality. a <2a <0 and, for every negative real number x, a > x This result contradicts the assumption that a is the greatest negative real number ✓ ✓ Therefore the supposition is false and the given statement is true.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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