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Thread: Multiplication number line?

  1. #1 Multiplication number line? 
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    The basic real number line is shown with 0 in the middle, +integers to the right, -integers to the left.

    This is based on +/- inverses, and 0 is in the middle because it has no opposite (or is its own opposite). Adding opposites yields 0.

    Instead of +/- opposites, what about a number line based on reciprocals?

    ... | | | | ...

    Of course, 1 would have to be in the middle, since it's its own reciprocal. Multiplying reciprocals yields 1.

    Is the idea correct? On a coordinate plane, if 1 is the origin, how different would functions look?


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  3. #2  
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    Ok. Thinking about this, wouldn't a coordinate grid of this make the rational function look linear?


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  4. #3  
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    What is your point? It seems that your number line wouldn't have negative numbers. Also it is not clear what your spacing is.
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  5. #4  
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    Sorry about this. Just another one of my speculative ideas. It does seem pointless; I apologize.
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  6. #5  
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    Okay, I put it onto a sheet of paper. And it works as I thought it would.

    You're correct, the number line can only show + or - numbers at a time. As such, the coordinate grid will only represent the real values of one quadrant into the normal grid.

    The number line is arranged as 0 ... 0.2, 0.25, 0.(3), 0.5, 1, 2, 3, 4, 5 ... with equal spacing between those intervals.

    The coordinate grid will be in like manner, with 1 at the origin. Here's a visual of the coordinate grid:



    Now try graphing and . They're analogous to and

    Because of definitions of iterations, operations represent each other in predictable ways. Using this, I hope to get an idea of hypothetical zeration.
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