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
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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.
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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 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.
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.
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