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Old 01-26-2008   #7 (permalink)
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Post Arithmatic expression vs. set description connotation of the square root

I think we’ve had essentially this same discussion before.

The root of the dilemma, I think, is that the square root glyph can be interpreted several ways.

\sqrt{x} can be considered simple equivalent to x^{\frac12}, e^{\frac12 \ln x}, or various infinite series expressions, in which case its sign is positive.

Or, \sqrt{x} can be considered the description of a set, \{ a : x = a \cdot a \}, which is equivalent to \{ -\sqrt{x}, \sqrt{x} \}.

As long as writer and reader are aware of which connotation is appropriate for the use to which the glyph is being put, there should be no problem.


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