Abstract
After analysing the skeleton of a mathematical proof, we survey the typical forms of a mathematical argument: implications, conjunctions, contradiction, the use of counterexamples to disprove statements. Then we turn to the effective delivery of an argument. We present examples of poorly written proofs; they are analysed in detail and then re-written with improved coherence, clarity, and style.
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Notes
- 1.
Abbreviation for the Latin quod erat demonstrandum, meaning ‘which had to be demonstrated’.
- 2.
If a prime divides the product of two integers, then it divides one of the factors.
- 3.
This result, known as Wilson’s theorem, was first formulated by Bhaskara (a 7\(^{\text {th}}\) Century Indian mathematician) and first proved by Lagrange.
- 4.
This phenomenon has deep roots, see [9, p. 155].
- 5.
Christian Goldbach (German: 1690–1764).
- 6.
Latin for ‘it does not follow’.
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© 2014 Springer-Verlag London
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Vivaldi, F. (2014). Forms of Argument. In: Mathematical Writing. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-4471-6527-9_7
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DOI: https://doi.org/10.1007/978-1-4471-6527-9_7
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Publisher Name: Springer, London
Print ISBN: 978-1-4471-6526-2
Online ISBN: 978-1-4471-6527-9
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