Im studing for the GRE math subject test...i can´t get the followin problem:
Using Mathematical Induction, show that it is possible to color with only two colors the regions formed by n lines in the plane.
Any idea on how to aproach it?
2026-02-25 01:52:04.1771984324
¿Mathematical induction GRE math?
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HINT: When you add an $(n+1)$-st line to a plane that already has $n$ lines and has been suitably colored, you can invert the colors on one side of the new line. (By invert the colors I mean change blue regions to red and red to blue, if blue and red are the two colors.)