Common Errors in Writing Mathematics

Common Errors in Writing Mathematics - Common Errors in...

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Unformatted text preview: Common Errors in Writing Mathematics The following things are often confused: equations, expressions, functions. An equation is a statement that two things are equal, like x 3 + 3 x- 2 = 0 or y = x 2 . An expression is some mathematical symbolism without a verb in it, for instance x + 1 or ( x + 1)( y- 2) or f ( x + a )- f ( x ) a . By “verb” I don’t necessarily mean something written as a word; more likely it will be an equal sign, or an inequality sign. A function is a process that takes inputs and makes outputs. The symbol f denotes a function, but f (3) does not; f (3) is a result or value of a function. So, do not refer to the “function f (3)”. You mean “the value f (3)” or “the output f (3)”. Exception. You may refer to “the function f ( x )” instead of “the value f ( x )”. This usage is technically incorrect, but accepted. The point is, x is a dummy variable here. You are merely saying that f is a function because it applies to inputs, rather than referring to the specific output when the specific letter x is input. Similarly, if z is your dummy variable, you may refer to “the function g ( z )” instead of “the value g ( z )”. However, in both cases it would be better)”....
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This note was uploaded on 05/04/2011 for the course MATH 73 taught by Professor Danberwick during the Spring '09 term at Berkeley.

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Common Errors in Writing Mathematics - Common Errors in...

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