Abstract
A statement in Mathematics is just a sentence which could be designated as true or false. The sentences “\(1 + 1 = 2\)” and “x = 4 implies x 2 = 16” are true statements while “All rational numbers are positive” and “There is a real number x such that \(x^{2} + 5 = 2\)” are false statements. Some sentences like “Green is nice” or “Authenticity runs hot” are too ambiguous, a matter of opinion, or are just plain nonsense and cannot be said to be true or false, so mathematicians would not consider them to be statements. Mathematicians have a lot of words for kinds of statements including many that you have heard: definition, axiom, postulate, principle, conjecture, lemma, proposition, law, theorem, contradiction, and others.
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© 2016 Springer International Publishing Switzerland
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Kane, J.M. (2016). What Are Proofs, and Why Do We Write Them?. In: Writing Proofs in Analysis. Springer, Cham. https://doi.org/10.1007/978-3-319-30967-5_1
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DOI: https://doi.org/10.1007/978-3-319-30967-5_1
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-30967-5
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