style - 1 x The sloppy constructs “ k ∈ Z ” and “ x...

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Stylistic requirements vary from circumstance to circumstance and from teacher to teacher. What may be normal usage in other circumstances or in more advanced classes, may not be acceptable in a class whose primary focus is learning syntax and good style. Summary: Get into the habit of using QUANTIFIERS! Example 1. The sentence n is an even integer if n = 2 k, k Z . is NOT acceptable. The required formats use QUANTIFIERS: n is an even integer if n = 2 k for some k Z . OR, using the terse language of formulas: n is an even integer if ( k Z ) n = 2 k. The next example explains why being fussy in the previous example made sense: Example 2. The sentence e x 1 + x, x R . is unacceptable. The required format uses quantifiers: e x 1 + x for all x R . OR ( x R ) e x
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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 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.

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