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1. Get examples of: o a theorem with a direct proof, and o a theorem with an indirect proof. The proofs should be short and simple.

1. Get examples of: o a theorem with a direct proof, and o a theorem with an indirect proof. The proofs should be short and simple.

Advanced Engineering Mathematics
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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1. Get examples of: o a theorem with a direct proof, and o a theorem with an indirect proof. The proofs should be short and simple. You may use proofs that are already published in literature or online references. Make sure you indicate the references.
Transcribed Image Text:1. Get examples of: o a theorem with a direct proof, and o a theorem with an indirect proof. The proofs should be short and simple. You may use proofs that are already published in literature or online references. Make sure you indicate the references.
2. For each proof, examine the following and highlight the specific sections in the proof. You may also give brief descriptions or explanations. • At which part of the proof are the premises used? Simply highlight in the proof the section where the premises are used. • Which valid argument forms are used in the proof? The proof might contain several valid argument forms. It is enough to specify ONE valid argument form in the proof. • What results other than those in the premises are used in the proof? Several "a priori" mathematical results might have been used in the proof. It is enough to specify ONE such prior result in the proof. You may also indicate ONE prior mathematical concept that have been used but is not indicate in the premises.
Transcribed Image Text:2. For each proof, examine the following and highlight the specific sections in the proof. You may also give brief descriptions or explanations. • At which part of the proof are the premises used? Simply highlight in the proof the section where the premises are used. • Which valid argument forms are used in the proof? The proof might contain several valid argument forms. It is enough to specify ONE valid argument form in the proof. • What results other than those in the premises are used in the proof? Several "a priori" mathematical results might have been used in the proof. It is enough to specify ONE such prior result in the proof. You may also indicate ONE prior mathematical concept that have been used but is not indicate in the premises.
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