The following “Theorem” is obviously not true. Explain what’s wrong with the proof. [5] Theorem: 1 is the largest natural number.Proof: The proof is by contradiction. Let n be the largest natural number, and suppose that n > 1. Multiplying both sides of this inequality by n we see that n2 > n. Thus n2 is a natural number greater than n, contradicting the fact that n is the largest natural number. So the assumption n > 1 is wrong, and therefore n = 1. So 1 is the largest natural number. 19:10 Fri 21 OctBackhttps://qmplus.qmul.ac.uk/1. The following "Theorem" is obviously not true. Explain what's wrong with the proof.Theorem: 1 is the largest natural number.Proof: The proof is by contradiction. Let n be the largest natural number, and suppose that n > 1.Multiplying both sides of this inequality by n we see that n²>n. Thus n² is a natural number greaterthan n, contradicting the fact that n is the largest natural number. So the assumption n> 1 is wrong,and therefore n = 1. So 1 is the largest natural number.2. Prove the following statements by contradiction.Theorem.83%(a) There do not exist integers x and y such that 15x + 1 = 21y.(b) There is no integer n such that n² + 1 is divisible by 4.[[

We see in the proof that it is a fact that n2 > n when n > 1. That means n2 is larger than n…

The following “Theorem” is obviously not true. Explain what’s wrong with the proof. [5] Theorem: 1 is the largest natural number. Proof: The proof is by contradiction. Let n be the largest natural number, and suppose that n > 1. Multiplying both sides of this inequality by n we see that n2 > n. Thus n2 is a natural number greater than n, contradicting the fact that n is the largest natural number. So the assumption n > 1 is wrong, and therefore n = 1. So 1 is the largest natural number.

The following “Theorem” is obviously not true. Explain what’s wrong with the proof. [5] Theorem: 1 is the largest natural number. Proof: The proof is by contradiction. Let n be the largest natural number, and suppose that n > 1. Multiplying both sides of this inequality by n we see that n2 > n. Thus n2 is a natural number greater than n, contradicting the fact that n is the largest natural number. So the assumption n > 1 is wrong, and therefore n = 1. So 1 is the largest natural number.

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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