1. 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?

2.

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

4. What is your point? It seems that your number line wouldn't have negative numbers. Also it is not clear what your spacing is.

5. Sorry about this. Just another one of my speculative ideas. It does seem pointless; I apologize.

6. 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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