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.
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.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Transcribed Image Text: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.
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