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-1 -.03

-1 -.03. 0. 1. 1.3 2.

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-1 -.03

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  1. -1 -.03 0 1 1.3 2 Project the real number line from [0,1] up above (the blue dotted lines), and draw a ½ ellipse connecting the end points of the projection. Pick any point on the real number line and draw a straight line from it to the midpoint on the projection (these are the red lines). Wherever the red lines hit the ellipse, draw a straight line up to his the [0,1] projection (these are the black dotted lines). Thus, every point on the real number line can be shown to have a one-to-one correspondence to a point on [0,1]. This proves that the infinity of points on [0,1] equals the infinity of points on the whole real number line, stretching infinitely in both directions

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