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Unformatted text preview: 1 + x. The sloppy constructs , k Z and , x R above denoted for some. .. in one situation and for all. .. in the other. This kind of ambiguity is unacceptable. Remark: The words with, where, for (in itself), often play the same unacceptable roles as the separating commas did above: n is an even integer if n = 2 k, where k Z . n is an even integer if n = 2 k for k Z . are as unacceptable as the comma version is. Use quantiers! These three words should be used only in special circumstances (e.g., in denitions). Using explicit quantiers is always the preferred way and most often the required way too....
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 Spring '08
 ctw
 Math

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