Unformatted text preview: or ), the author simply states the extra hypothesis (e.g., “Assume Statement A” or “Assume Statement B”). Then, when starting the other direction of the proof, the author might say something like “Conversely assume Statement B” or “Conversely assume Statement A”. The importance of a theorem of this type, once proved, is that Statements A and B are equivalent in the sense that, under the general hypotheses, they either are both true or both false, that is, it is impossible to have one of them be true and the other false. This is a very useful type of result....
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 Spring '11
 Brigham
 Formal language, Typetoken distinction, general hypotheses

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