Can the number of tangents from a point be more than one?
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I could agree with my friend too, but if we take a curve to be y=x2y=x2 and tangent to be y=0y=0than there is no point except (0,0)(0,0) that is common to them.
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No point in any small neighbourhood around (0,0)(0,0) is common to both. That seems to only reinforce myself.
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