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 quantiﬁers! These three words should be used only in special circumstances (e.g., in deﬁnitions). Using explicit quantiﬁers is always the preferred way and most often the required way too....
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This note was uploaded on 01/31/2011 for the course MATH 300 taught by Professor Ctw during the Spring '08 term at Rutgers.
 Spring '08
 ctw
 Math

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