Suppose you are building a mathematical theory, and you come up with a proof that a certain statement is true. Later, you come up with a proof that the negation of the same statement is true. Which of the following cannot possibly be the case? O Your entire theory is flawed because it contains a contradiction. O One or more of the proofs you have done up to this point contains a flaw. O Your set of axioms is inconsistent. O This always happens sooner or later in the process of mathematical theory-building, and it's nothing to worry about.

Suppose you are building a mathematical theory, and you come up with a proof that a certain statement is true. Later, you come up with a proof that the negation of the same statement is true. Which of the following cannot possibly be the case? O Your entire theory is flawed because it contains a contradiction. O One or more of the proofs you have done up to this point contains a flaw. O Your set of axioms is inconsistent. O This always happens sooner or later in the process of mathematical theory-building, and it's nothing to worry about.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.2: Mathematical Induction

Problem 49E: Show that if the statement is assumed to be true for , then it can be proved to be true for . Is...

See similar textbooks