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2.8: Summary

  • Page ID
    62279
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    Summary

    • A “two-column proof” is a tool that we use to learn techniques for writing proofs.
      • The left-hand column contains a sequence of assertions.
      • The right-hand column contains a justification for each assertion.
      • Each row of the proof is numbered (in the left margin) for easy reference.
      • A dark horizontal line is drawn to indicate the end of the hypotheses.
      • A dark horizontal line is drawn along the left edge of the proof, and of each subproof.
    • In addition to the basic theorems of , we have two rules that use subproofs:
      • \(\Rightarrow\)-introduction
      • proof by contradiction
    • Proofs often use the Law of Excluded Middle, the Rules of Negation, and contrapositives.
    • Assertions that are in a subproof cannot be used as justification for lines that are not in that same subproof.
    • Writing proofs takes practice, but there are some strategies that can help.
    • Proofs can also be written in English prose, using sentences and paragraphs.
    • To show that a deduction is not valid, find a counterexample.

    This page titled 2.8: Summary is shared under a CC BY-NC-SA 2.0 license and was authored, remixed, and/or curated by Dave Witte Morris & Joy Morris.

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