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> Mathematical Operations On Ranges?
StevensElectronicAccount
Posted: April 30, 2011 06:00 pm
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Hi. Usually a pair of numbers is used to represent a Cartesian point. Using imaginary numbers one point might be, 1 + j2.
This representation very naturally extends a lot of the math.
I'm wondering can something similiar to complex numbers represent ranges of values on a line?
For example, to represent the range from 1 to 2 I'd use 1 + j2.
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Sch3mat1c
Posted: May 01, 2011 12:12 am
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Well if you want just the endpoints, you can use a pair, such as a vector or matrix.

What is your intent? If you are interested in what happens to all points within the interval, you operate on that interval with a function defined over that range. This is generally noted as "f : x --> y", read "[function] f is a transformation from [set of points] x to y". If, for instance, you are analyzing the transformation of a function over that range, you compose them (i.e., f(g(x))).

If you are only interested in tracking the endpoints, then only the numbers (and the value of the transformation at those points) is sufficient. For instance, if you wanted to compute linear transformations on line segments, you only need the endpoints. You would do this for rotation, scaling and perspective transformation of a three-dimensional scene into a two-dimensional representation (which, incidentally, is an example of a multivalued transformation, because there are an infinite number of points (indeed, along rays extending from the viewpoint) which result in the same screen coordinates.

Tim


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Answering questions is a tricky subject to practice. Not due to the difficulty of formulating or locating answers, but due to the human inability of asking the right questions; a skill that, were one to possess, would put them in the "answering" category.
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