This question relates to linear programming problems.
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Consider the constraints y≥-x, y≥x and y≥ε and make ε as small as you want.
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@Issledovatelnitsa: well, there is nothing really clever. Take two points as close as you want, and let three lines go through them. – Mar 13 '22 at 17:34
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@Issledovatelnitsa: in a Ukranian pub ? – Mar 15 '22 at 07:45