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The Grammar According to West
I have been accumulating observations about writing mathematics for many years. These conclusions arose both from writing textbooks and from noting writing errors commonly made by my thesis students and in papers submitted to journals.
In contrast, "we may assume" introduces a consequence of an argument or symmetry and henceforth will be true. After words of hypothesis or conclusion ("suppose", "assume", "implies", "conclude", etc), use "that" when what follows is a clause with an English verb. For example, "Assume the hypothesis" is a complete sentence with imperative verb and object.
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