The n- dimensional space is colored with n colors such that every point in the space...

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Advance Math

The n- dimensional space is colored with n colors such thatevery point in the space is assigned a color. Show that there existtwo points of the same color exactly a mile away from eachother.

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For n1 there is nothing to prove For n consider n1 points p0 p1pn in Rn all at a distance of 1 mile from each other which are affine independent ie p0 p1 p0 p2 p0 pn are linearly See Answer

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The n- dimensional space is colored with n colors such that every point in the space...

50.1K

Verified Solution

Question

Advance Math

The n- dimensional space is colored with n colors such thatevery point in the space is assigned a color. Show that there existtwo points of the same color exactly a mile away from eachother.

Answer & Explanation Solved by verified expert

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