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C - How to prove that …

from Appendices

Kevin Houston
Kevin Houston
Affiliation:
University of Leeds
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Summary

It is impossible to give an algorithm that will prove any statement. However, in some cases there are strategies that we can pursue first. In this appendix we give a summary of how to prove various types of statements. Examples are eschewed in favour of brevity.

How to prove that one statement implies another

To prove that A implies B try a number of methods.

  • A direct sequence of implications signs.

  • Prove the contrapositive statement: prove that the negation of B implies the negation of A.

  • Contradiction: Assume the statement is false and prove that this leads to an absurd statement, such as 0 = 1.

    • Type
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    How to Think Like a Mathematician
    A Companion to Undergraduate Mathematics
     , pp. 260 - 262
    Publisher: Cambridge University Press
    Print publication year: 2009

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    • How to prove that …
    • Kevin Houston, University of Leeds
    • Book: How to Think Like a Mathematician
    • Online publication: 05 June 2012
    • Chapter DOI: https://doi.org/10.1017/CBO9780511808258.039
    Available formats
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    • How to prove that …
    • Kevin Houston, University of Leeds
    • Book: How to Think Like a Mathematician
    • Online publication: 05 June 2012
    • Chapter DOI: https://doi.org/10.1017/CBO9780511808258.039
    Available formats
    ×

    Save book to Google Drive

    To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

    • How to prove that …
    • Kevin Houston, University of Leeds
    • Book: How to Think Like a Mathematician
    • Online publication: 05 June 2012
    • Chapter DOI: https://doi.org/10.1017/CBO9780511808258.039
    Available formats
    ×