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Plane Geometry is about flat shapes like lines, circles and triangles , shapes that can be drawn on a piece of paper

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Subset of the plane that intersects every line exactly twice

By AC, choose a cardinal well-ordering of the lines in in the plane and any well-ordering of all the points. We proceed by transfinite induction. Suppose $A_l$ is a set of points, no three colinear, …
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