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In Example 1.2 we gave a proof of 1+1 = 2 in seventeen proof steps. At that point you may have asked yourself: If it takes that much effort to prove such a simple statement, how can one ever prove any non-trivial mathematical result using formal proofs? This objection is of course justified; however, we will show in this chapter how one can simplify formal proofs using some methods of proof such as proofs by cases or by contradiction.

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The Art of Proof

  • 章节

  • 发表日期：

    2025年

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  • Lorenz Halbeisen,
  • Regula Krapf

摘要

In Example 1.2 we gave a proof of 1+1 = 2 in seventeen proof steps. At that point you may have asked yourself: If it takes that much effort to prove such a simple statement, how can one ever prove any non-trivial mathematical result using formal proofs? This objection is of course justified; however, we will show in this chapter how one can simplify formal proofs using some methods of proof such as proofs by cases or by contradiction.